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Foden struck twice as Manchester City stepped up their bid for a fourth Premier League crown in a row with a ruthless 4-0 victory at Brighton & Hove Albion.
Everton's first derby victory at Goodison Park in more than 13 years prevented Liverpool from climbing level with Arsenal at the top of the league table. Juergen Klopp's men are three points behind the Gunners (77) with four games to play.
It was the sixth time Arsenal have scored five or more in a Premier League game this season without conceding and in such a tight race they now have a huge goal difference advantage which could prove crucial to the outcome.
Arsenal lead on 74 points, one point ahead of Manchester City.
The heavy defeat leaves Everton 16th on 27 points, two places and two points above the relegation zone.
Arsenal's defeat, their first in 12 league games, sees them remain second, two points behind City and level on points with third-placed Liverpool with six games left to play.
Pep Guardiola's men have 73 points with six games remaining in a rip-roaring three-way title race, two points ahead of both Arsenal and Liverpool, who can climb over City with victories in their respective games on Sunday.
With seven games remaining in the neck-and-neck title race, Liverpool and Arsenal have 71 points with the Gunners leading on goal difference. Holders Manchester City are third on 70 points, while United are sixth.
Arsenal's 10th win in their last 11 league games put them on 71 points from 31 games.
Juergen Klopp's side have 70 points from 30 games, two ahead of Arsenal and three more than champions Manchester City.