The eight-time champion lost just five points in a 16-minute first set but faced break points for the first time in this year’s tournament, saving all four
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Federer was in blinding form during the first set, which blazed by in 16 minutes.
The match was postponed after the marathon battle between Rafa Nadal and Gilles Muller ended late on Monday on Court One.
Tsonga was making his return after the birth of his first child, but in the opening second round match of the week, the Frenchman crashed out 6-7 (3-7) 6-2 6-3 against his fellow countryman and world No 56