(CNN) What do you get when you put Lindsey Vonn and Roger Federer together on the ski slopes of St. Moritz?

Two mountain GOATs, of course.

Two of the "greatest of all time" joined up Sunday, as tennis ace Federer watched ski queen Vonn race to the seventh World Championships medal of her illustrious career.

Vonn's bronze in the downhill -- at 32, she is the oldest female skier to win a medal at the biennial competition -- came just a month after her return from a broken arm and severe nerve damage in her right hand.

The US star credits Federer as inspiration after the Swiss came back from a lengthy knee injury layoff to win the Australian Open in January -- his 18th grand slam title -- at the age of 35.

"He's still here. I'm going to go say hi, don't tell anyone. I love 'Rog,'" Vonn, 32, told CNN's Alpine Edge. "He's the best. He won in Australia and I feel like a lot of people counted him out because he's 'old.' And he won.

"I get so much inspiration from that. He's such a humble person but he has so much heart. He always gives everything he has. I try to emulate that in myself, in my skiing, in my career.

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"To have him come here and watch me ... this is the first time he's ever watched me race and I've been to many of his tennis tournaments so this is very, very nice. I think this is the icing on the cake for today.

"I mean, at some point he had to come watch me. It was about time."

Vonn revealed in January that her broken arm -- suffered during training in Colorado in November -- caused nerve damage so severe she couldn't even move her right hand.

The extent of her injury was still apparent Tuesday when a loss of grip on her pole caused her to get distracted and ski out of the super-G. She taped her pole to her hand for Friday's alpine combined, where she came fifth.

'No control'

"It's been a struggle. More so emotionally than anything else," the 2009 world downhill champion and 2010 Olympic champion said.

"Just having no control over a body part is difficult, especially your right hand.

"You don't realize how much you use your right hand until you don't have it anymore. Just the simplest things like eating my food, shaking hands or signing autographs were difficult.

"Getting over that and at least be able to shake people's hand and do stuff like that was a huge step in the right direction, so it's not as good as it could be but it's good enough.

"I'll keep working on it so hopefully I won't have a messed up hand forever."

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Despite being winning 77 World Cup races -- second only to Ingemar Stenmark's 86 -- Vonn insists her downhill bronze in St. Moritz was one of the sweetest medals of her career.

"It's amazing. I couldn't be happier," Vonn said.

"I had no training and hardly any self-confidence. It was hard to come here and really attack but I did. The bronze honestly feels like gold. It's my seventh World Championship medal.

"I couldn't be happier. This is probably one of the most meaningful medals of my career."

Swiss mountain GOAT?

An avid skiing fan growing up, Federer spent the day celebrating compatriot Beat Feuz's gold in the men's downhill, before watching Vonn secure her bronze.

Federer is widely considered tennis greatest of all time ... but is he a mountain GOAT?

"I'm actually more of a beach guy, if you like it or not," he replied. "I get so cold in the snow and the mountains like this. But it's super powerful to be here in the nature and I love spending time here.

"The World Championships taking place in St. Moritz is a thing I didn't want to miss. Yesterday we were having fondue and after the third glass of wine we were like, 'Shall we go to St. Moritz tomorrow?'

"'I don't know, let's see if we can get tickets.' So I made a few phone calls and then my dad called me this morning saying they have tickets. We had the best day. I'm happy we chose to come today."

Federer says Vonn offered to teach him how to ski ... so how about a lesson from one of the greatest skiers of all time?

"She has yes, but no... I can't do it at the moment," he said. "She should take my kids out skiing rather than myself. I'm too scared at the moment.

"That's not how I want to finish my career, in a skiing accident."