With more Grand Slam titles than any man in history, Roger Federer had nothing to prove when he strode onto Centre Court for Friday’s Wimbledon semifinal against defending champion Novak Djokovic.

But in dethroning the world No. 1 in four swift sets, Federer proved plenty. Namely: Age has not diminished his skill; grass is the surface that showcases his gifts most supremely; and he remains, at 30, a formidable threat to add to his cache of 16 major championships.

To the utter joy of Britain’s sporting public, Scotland’s Andy Murray is the man he’ll have to beat to do so, finally reaching Wimbledon’s final after suffering three consecutive semifinal knockouts.

With his 6-3, 3-6, 6-4, 6-3 victory, Federer advanced to his eighth Wimbledon final, a record not even Pete Sampras holds.

And in turning back Jo-Wilfried Tsonga, 6-3, 6-4, 3-6, 7-5, Murray touched off a jubilant celebration on the grounds of the All England club, where thousands packed the hillside known as “Murray Mound” to groan and exult via a giant projection screen.

Given Britain’s 74-year wait for a Wimbledon finalist, the BBC’s Tom Fordyce predicted that Murray’s clash with Tsonga, a wildly talented Frenchman who upset Federer to reach last year’s semifinals, would be “a ghastly, glorious nerve-shredder.”

And when Murray ripped a winning service return cross-court to end the match, confirmed seconds later by instant replay, the hillside erupted in cheers. Union Jacks and Scottish flags fluttered. Umbrellas turned into parasols that punctuated jubilant dances. And chants of “Ahn-DEE!” “Ahn-DEE!” filled the air, loud enough for Murray to hear inside Centre Court, where Tsonga wrapped him in a congratulatory embrace. The crowd of 15,000 stood in tribute to Murray, 25, the first British man to reach Wimbledon’s final since Henry “Bunny” Austin, also known as the first man to compete in short pants, did so in 1938.

Friday’s men’s semifinals consisted of four of the tournament’s top five seeds, the notable absentee being two-time champion Rafael Nadal. His second-round ouster was deemed a boon for Murray, who’d been sent packing by the Spaniard the last two years.

But the big-serving Tsonga was hardly an easy out.

Murray started well, committing just four unforced errors through the first two sets compared to Tsonga’s 20 and pinning his opponent on the baseline with deep, well placed groundstrokes.

“He didn’t give me one chance to go the net,” said Tsonga, 27, who relishes playing the aggressor.

After falling behind two sets to none, Tsonga left the court for treatment on his back and came back rejuvenated. Murray fell flat and lost his serve and the third set. The fourth set was higher-caliber stuff, with the only break coming in the 12th and decisive game.

Murray was restrained in victory, burying his head in his fists, then raising his index fingers to the sky. His coach, Ivan Lendl, betrayed no emotion from a courtside box.

Lendl, 52, famously lost four Grand Slam finals before winning his first. If Murray falls short Sunday, he’ll also have lost four without a victory. Both know his work is not finished.

“It’s a massive challenge to win against Roger in the final of a slam, at Wimbledon,” Murray said.

After Friday, Djokovic would agree. Though Federer held a 14-12 edge in their rivalry, Djokovic was favored in their first meeting on grass. The Serb won their last three meetings, including the semifinals of last year’s U.S. Open, in which he fended off two match points.

The first two sets raced by quickly. Hardly a point was settled by a rally but rather aces or outright winners on the first or second strike.

The third set was worth the price of admission, even at scalpers’ inflated prices, with two long rallies in the sixth game showing off the offensive and defensive genius of both men.

“In the important moments, he was aggressive,” Djokovic conceded afterward. “I needed to be very consistent in order to win this match. I wasn’t.”

And when Federer sealed the victory with his 31st winner, he was as economical with his emotions as he was with his strokes.

It has been two-and-a-half years since the Swiss won a major, the 2010 Australian Open. With a victory Sunday, he would match Sampras’s open-era record of seven Wimbledon titles, as well as reclaim the No. 1 ranking one month shy of his 31st birthday.

Said Federer: “I’m aware that the tournament’s not over.”

Notes: Agnieszka Radwanska, who’ll face Serena Williams in Saturday’s women’s final, withdrew from her doubles match and canceled a press conference Friday, citing an upper respiratory ailment. . . .

Serena and Venus Williams upset the top-ranked doubles team of Lisa Raymond and Liezel Huber, 6-2, 1-6, 6-2, to advance to Saturday’s championship. It will be the day’s third match on Centre Court, following the women’s singles and men’s doubles finals. . . .

Americans Bob and Mike Bryan were denied a chance at a third Wimbledon title, falling in the men’s doubles semifinals to Britain’s Jonathan Marray and Frederik Nielsen of Denmark, 6-4, 7-6 (11-9), 6-7 (7-4), 7-6 (7-5).