The successful appeal means he is cleared to take part in Aston Villa's next match against Manchester United on April 5.
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Aston Villa manager Martin O'Neill disagreed with the decision and said: 'I've seen the sending off from a better angle and, from Brad's point of view, I don't think he's gone out and made a deliberate attempt to upend him.
'In fact, quite the opposite. When Torres touched the ball on, Brad realised he wasn't going to get it and actually made himself smaller.'
Aston Villa have dropped to fifth position after allowing Arsenal to overtake them and go three points clear, and will be grateful to have Friedel reporting for duty.
The clash at Old Trafford will provide a stern test for O'Neill's men as they seek to get their season back on track.
United's title credentials will be heavily scrutinised by playing a side that Liverpool so comprehensively beat.