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Chelsea completed the double over AC Milan to top Champions League Group E with a 2-0 victory at San Siro on Tuesday.
City drubbed Southampton 4-0 with Erling Haaland scoring again.
An insipid Milan failed to show any sort of response, barely putting the home defence under pressure, let alone threatening a goal, as Chelsea strolled through the final half-hour.
Arsenal posted a 3-1 win over 10-man Tottenham at the Emirates Stadium.
Announcement comes a day after EPL team lost 1-0 to Croatian team Dinamo Zagreb in its opening game of the Champions League group stage.
Erling Haaland scored again but Gerrard's Aston Villa secured a 1-1 draw against Manchester City.
League leaders Arsenal scored late to beat Fulham 2-1 in the premier league.
Tuchel played down the bad blood between him and Conte during and immediately after the game.
Chelsea manager Thomas Tuchel and his Spurs counterpart Antonio Conte were both shown red cards after the final whistle as tempers boiled over on a sweltering afternoon in west London.
A penalty on the stroke of half-time from Jorginho was enough to give Chelsea a hard-fought 1-0 win at former favourite Frank Lampard's Everton.
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