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The former world number one took control of the court in the opening set by earning an early break of serve, leaving Tsonga on the backfoot from the off.
Courtesy of some gliding shots and 11 winners, Federer was about to wrap up the first set, but he was faced with some competition in the second set when Tsonga regained his composure.
The Frenchman managed to keep hold of his service games and nab four aces of his own before Federer was able to grab one break point to push on and take a two-set lead.
Federer continued his dominance in the third set by grabbing another break point, and while Tsonga continued to push, Federer was able to hold off the pressure and seal a place in the next round.
Federer will take on Andy Murray for a place in the semi-finals.