Second seed Federer will face Andy Murray in the last four at SW19.
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The seven-time champion asserted himself early on by breaking Simon before taking a 3-0 lead. Despite a rain delay during the opening set, Federer kept the Frenchman at arm's length on his way to taking it 6-3.
It was a similar tale in the second as the Swiss broke to establish a 5-4 advantage thanks to some ruthless groundstokes and decisive touches at the net.
However, Simon broke back to level things up at 5-5 - the first time that Federer has dropped serve in 116 service games. With the 12th seed now looking as if he was about to halt Federer's dominance in the match, the 33-year-old broke back instantly on his way to closing out the set 7-5 after a rain delay.
Simon's limp challenge looked to be all but over when he slipped 0-2 behind at the start of the third, and from there Federer was able to keep his momentum and secure a 6-3 7-5 6-2 triumph.