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That's all from me today.

Tune into Match of the Day 2 from 22:35 BST on BBC One for highlights on all the games, including goals from yesterday.

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In case you joined us late, here's what's happened in the Premier League today. Click on the links to read match reports from all four games.

Crystal Palace had to settle for a draw following a late equaliser from Wolves earlier today, while West Ham recorded a 2-0 win over a struggling Manchester United.

Arsenal came from behind in emphatic style to beat Aston Villa at home and Liverpool held on despite a late onslaught from Chelsea to remain five points clear at the top.

And here's what happened yesterday.

Arsenal

More from Unai Emery, speaking to Sky Sports, on Ainsley Maitland-Niles' second booking which led to his sending off:

"I was thinking we can manage. He didn't touch the player. He touched the ball. We had to accept the referee's decision."

Arsenal

Arsenal boss Unai Emery, speaking to BBC MOTD: "90 minutes a lot of things happened. When it was 11 v 11 we didn't control the match how we wanted because we lost a lot of balls in the middle and gave them chances in the transition. When we could attack and get the ball in the box we weren't bad really. We were also creating chances to score. After the goal we could be calm and improve and the red card changed the idea. For the second half we needed to play first with the head but also with our heart. We needed supporters pushing us and us to take some risks. The team spirit was amazing. We need to continue working and improving things.

"Aston Villa is a good team and an organised team. After this I hope we can improve and be strong. Together with the supporters we will be strong for the matches and hopefully improve.

"It is out challenge to improve defensively. They didn't have a lot of chances to score."

Liverpool

Liverpool boss Jurgen Klopp, speaking to MOTD: "The first half was also hard work. It is about momentum in games like this and I think we got that in the first half. We scored two wonderful goals and we could have scored directly after half time two more. We deserved the three points, it is a difficult to win here."

"We are only here. Chelsea, six matches in. We haven't won anything domestic apart from games so we have to carry on. We have to be ready for each opponent. They are all waiting and want to give us a knock, rightly so but we have to be ready to do what we have to do."

On Adrian: "We all have weaknesses, a goalie has weaknesses but he has really settled in the team and he made a few outstanding saves today. We would not have signed him if we did not think he could do the job."

Aston Villa

More from Aston Villa boss Dean Smith to Sky Sports: "We will never get a better chance to win at the Emirates. Going a goal up and they went down to 10 men. We retracted when we should have gone out to get the second. We have made a mistake.

"We have given them three goals and dropped too deep in the second half, hanging on to the lead we had. Just before half-time I thought it became a bit of a basketball game - it was end-to-end. We didn't make the most of our opportunities and lost our structure.

"We ended up jumping out from midfield and they played through us. It is a bitterly disappointing dressing room as they know they can compete but we lost belief in the second half.

"I don't see too many positives at the moment but in the cold light of day we will look back and analyse the game. The home games are going to be very important. We have had opportunities in all games and not fear anybody except maybe the Man City's and Liverpool's in this league.

"We took the lead against Tottenham, should have got a point against Crystal Palace and should have taken something from this game. It's just about having a bit of know-how."

Chelsea

Chelsea boss Frank Lampard on Sky Sports: "Performance wise we were the better team. We had more energy in our game, character and spirit. That’s why the crowd applauded at the end. Let's take this forward.

(On Mason Mount's disallowed goal): "I like to think we might get a couple in our favour. But you can see Mason is a tiny bit offside.

"We have to get on with it. It is a sad thing for the celebration and the moment but if we are looking for correct decisions that is where we are at. It changes the atmosphere in the crowd, on the pitch. We are slightly deflated and they get a boost. We deserved to be level at that point.

"No home wins we want to change and I believe we will if we play like that. The reality is younger players have come into the team. We lost two number 9s we had last year and we can't change that.

"People say the [transfer] ban is a bad thing for Chelsea and in the short term, of course, but in the long term if we can have a vision, with the likes of [Fikayo] Tomori, Mason [Mount], Tammy [Abraham], then hopefully it will be really good for us but in the short term there might be occasions with things like today happen."

Jahanzeb Khan: Chelsea have shown character and is showing that players are trusting the manager while Manchester United players and manager are at different wavelength which is resulting in poor performances.

Aston Villa

Aston Villa boss Dean Smith, speaking to BBC MOTD: "I am bitterly disappointed. We lost our structure for periods in the second half. First half we were on the front foot and looked solid. It is always going to be a tough game but we will never get a better chance to win.

The game became too open with them at 10 men. We lost our fearlessness but for some reason we retracted second half and put us under pressure. We scored again and had a good five min spell but retracted again. The players lost a bit of belief and that is what disappointed me the most.

"You look at the goals we conceded and they are sloppy. We concede a penalty and give a free-kick away. Second goal, Tyrone Mings has cushioned a header to Neil Taylor and should have put it out for a corner.

"I thought it was penalty (for handball against Sokratis). He leant towards the ball, which was going towards the goal. It has hit his arm so I don't know why it wasn't. But if you're asking about handballs in the box these days, I don't know and I don't think anyone knows. We have seen some subjective ones. If they get a good view on the TV screens they need to overrule the on-field referee."

On his side's form: "There is no big concern. We have had a real good go. Apart from Man City and Liverpool I don't fear anyone in this league."

Arsenal's 3-2 win over Aston Villa was only the ninth occasion in Premier League history a team has won a match after receiving a red card while losing - three of those wins have been by Arsenal (also v Derby in 1997 and Bolton in 2008).

The Gunners won a Premier League game they were trailing in at half time for the first time since December 2018 (4-2 v Spurs at the Emirates).

Aston Villa haven’t won any of their last five Premier League away games when scoring first (D1 L4), suffering defeats in each of their two such games in 2019-20 (1-3 v Spurs and 2-3 v Arsenal).

Bukayo Saka became the third-youngest player on the day of his first Premier League start for Arsenal, with only Cesc Fábregas (17y 104d) and Theo Walcott (17y 212d) doing so at a younger age.

Steve Tudor: Yeah we were rubbish. But we win. With 10 men. And we’re 4th. That’s the winning messily we need to be able to do.

Ben Symmonds: Cannot see why Arsenal fans slate Guendouzi, he's won a penalty, hit the post, kids only 20 give him a chance.

Aston Villa

Aston Villa striker Wesley speaking to FPL: "We are very disappointed. We had 11 men and Arsenal had 10. We have to win these games.

"For 60 minutes we played well. We scored a goal then stayed back and Arsenal scored three more goals.

"We have to work hard because you cannot lose like this."

Chelsea

Chelsea defender Cesar Azpilicueta, speaking to Sky Sports: "Very disappointed with the result but we knew at half time we could hurt them a lot. When you are 2-0 down it is hard but the team pushed and the fans pushed. We were unlucky not to get something from the game.

On the VAR ruling out his goal: "I was in the box. I made the call and you don't think it is going to be offside because the action was not a clear offside. With VAR you get a big disappointment because that could have been a big turning point in the game at 1-1 but then we concede the second goal.

"We are more and more used to VAR. What can you do? You have to celebrate the goal even if sometimes you risk it to be disallowed. We have to be used to it and get on with it.

"We are Chelsea and we want to win games. This is the moment to go forward now and get more points."

Aston Villa

Aston Villa midfielder John McGinn, speaking to BBC MOTD: "That is two weeks in a row that teams down to 10 men have affected us badly. We have addressed it in the dressing room. I don't know if it is a lack of belief or tiredness, which it shouldn't be. We should be creating the chances but we weren't.

"We showed we are dangerous and scored a good goal, concede one and then show it again. But we got deeper and deeper and you can't do that. It is game management. It has cost us dearly this season. When you force pressure on yourself you get punished. We need to capitalise when things go for us in the game.

"We are yet to get a VAR decision go our way. There was no surprise that (a late penalty call for handball) didn't for us."

Liverpool

Liverpool captain Jordan Henderson to Match of the Day:

"It was tough but we knew it would be. Chelsea are a good side, play great football, but to come here, do the job, we are over the moon with that.

"We are delighted, we knew they would put us under pressure, we had a couple of chances ourselves.

"We go onto the pitch with confidence, with the mentality to work as hard as we can, chase them all over the pitch.

"We did that and got our rewards. That has to be every game and the next game is the biggest game."

Stuart Eccles: Simple stuff for next game, Chambers starts, Xhaka doesnt. If Holding is fit he starts as well. Guendouzi 1st choice with either Torreria / Willock then either Ozil or Ceballos. Saka also deserves to keep his place.

Ben Ashton: Arsenal aren’t good for my blood pressure.

Liverpool

Liverpool boss Jurgen Klopp, speaking to Sky Sports: "It was a good game between good sides. We forced the set-pieces in decisive areas. Second half I think we had two, at least one no-brainer to make it more clear and 3-0 would have been a statement in the Premier League but then N'Golo Kante makes his little run and kicks it in with his big toe.

"Then it is completely normal that you come under pressure but we defended well. There were a couple of good saves from both goalkeepers. Good situations in an exciting game and that is how it is in the top six and in the Premier League.

"We work on set pieces. All the things we do in training I love to see on the pitch. Big fight from everybody.

"Sadio [Mane] got a bad knock. He is OK but we have to make that substitution. You will never win at Chelsea without putting a proper shift in and we did that today.

"It is exceptional. What can I say? We have to keep on going. It is never looks as easy as it did for City yesterday but we have not had these games yet. We have to work for it."

Liverpool retain their five-point lead over Manchester City at the top of the table with that big result.

Arsenal are back into fourth place, while West Ham will be pleased despite being nudged back down into fifth.

Image source, BBC Sport

David E: Summary of Chelsea season so far: superb in one half and disappear in the other half. Not good enough.