Referee Chris Kavanagh was right to send Declan Rice off in Arsenal's draw with Brighton, the Key Match Incidents panel has ruled.
The board - which reviews the big refereeing decisions in the Premier League each week - agreed the midfielder should have been dismissed.
Rice, who was already on a booking, nudged the ball away from Joel Veltman as he prepared to take a free-kick in the 49th minute of Arsenal's 1-1 draw with Brighton last weekend.
It was the first red card of the England star's career, with the panel agreeing his actions were "clear, deliberate and impactful" and a second yellow card was correct.
The panel, which unanimously backed the decision, wrote: "Rice knows what he's doing - it's a gentle touch, but once the referee sees it he has no choice."
Arsenal were 1-0 up at the time after Kai Havertz's goal, but Joao Pedro's leveller earned Brighton a point at the Emirates.
The KMI panel is independent and made up of three former players or coaches, one Premier League representative and one from the Professional Game Match Officials Board, the referees' body.
It also ruled the video assistant referee (VAR) was right to intervene in Trent Alexander-Arnold's goal in Liverpool's 3-0 win at Manchester United.
The goal was initially given but was then ruled out, with Mohamed Salah deemed to have been offside in the build-up.
It was the only on-pitch decision ruled to have been incorrect out of the 23 looked into for match week three.
The panel was unanimous in its support of every on-field call, except the decision not to give Crystal Palace's Will Hughes a second yellow card in their 1-1 draw at Chelsea.
The midfielder, already on a booking, avoided a caution from referee Jarred Gillett despite pulling back Cole Palmer outside the box just after half-time.
The first caution was unanimously supported as correct, with the majority (3-2) supporting Gillett's decision not to issue a second yellow.
However, two of the panellists argued: "Palmer is the wrong side of Hughes and has options left and right, therefore it is stopping a promising attack
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