The action has continued from the Wimbledon quarter-finals with Germany's Julia Goerges beating a close friend to make the first semi-final of her career, while Juan Martin del Potro resumed his rain-interrupted match to set up a showdown with Rafael Nadal.
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Djokovic had told reporters that he had been hopeful of playing his quarter-final match on Centre Court before telling Serbian media that he "deserved" the honour and meant to lobby the All England Club.
With Kevin Anderson taking nearly three and a half hours to tame French showman Gael Monfils in the previous match, Djokovic knew he had about two hours of daylight left if he wanted to avoid coming back on Tuesday's rest day to finish off the contest. "I am happy to be where I am", Nadal said. "I feel like the more experienced you are, the more you can deal with those better". As for his level I think he looked decent but not in spectacular form, Vesely was a real disappointment though, his forehand was powder puff stuff, loopy and it just sat up waiting for Rafa to take charge. "Keep on going, you can do this".
"Wow, it's pretty awesome", Goerges said.
"I've often said the day that you don't feel nervous is the day you should be more anxious about".
I think their level is just so high that it will take one of them nearly freak players to beat them. It's never easy playing a friend. I thought it was a good scoreline, but it was tougher than the score, to be honest.
Later seven-time champion Serena Williams faces 52nd-ranked Camila Giorgi of Italy, and 13th-seeded Julia Goerges faces Kiki Bertens as the pair both play in their first Wimbledon quarterfinal. "But every match starts from zero". He had three break-point opportunities during the third set but saved them all.
The last-16 tie between Del Potro and Frenchman Simon was suspended overnight due to darkness on Monday with the Argentine fifth seed two sets to one ahead.
His 6-0, 7-5, 6-4 win against the No 22 seed from France extended his streak of sets won here to 32.
Anderson, who hit 20 aces on the day, reached his first Grand Slam final at the 2017 U.S. Open and had lost in the fourth round at Wimbledon on three previous occasions.
Simon, looking for his third Grand Slam quarter-final at the age of 33, secured the first break of the match to take a 4-3 lead in the second set when Del Potro netted a return.
Meanwhile, 2016 runner-up Milos Raonic and 2009 US Open champion Juan Martin del Potro are also in familiar territory.