How do I win over an otherwise all male team that don't like that a younger woman was promoted above them?

I'm just the team leader so barely above them, but at the same time I'm given total control over the team. I was explicitly told that I'd be supported if I wanted to make personnel changes in the team and that half of them they'd happily fire while the other half would just be moved around. I know a... show more I'm just the team leader so barely above them, but at the same time I'm given total control over the team. I was explicitly told that I'd be supported if I wanted to make personnel changes in the team and that half of them they'd happily fire while the other half would just be moved around. I know a bunch of women from my previous job that I think would be interested if it came to that Most of the team wanted the promotion, but everyone thought one guy was going to get it. Ironically, he is the only one being supportive of me. He's really sweet and he's the only one that calls me "boss" even though we all called our previous team leader that. There's been snide comments and insinuations that I only got the jobs because I'm a woman or because I slept with someone or because of my looks. I certainly didn't sleep with anyone.

There have also been comments that there was no way I deserved the job over the other guy, but he said to me himself that he thought I deserved it, but then maybe he is just being kind. I got on pretty well with these guys before the promotion, but the comments aren't stopping. I'm not sure how to handle this though. I'm worried I'll prove them right if I handle this badly though so I'm interested to hear any advice.
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