Bully at work. Thought work over months and coaching not helping

I have just received another email from a bully at work who copies in all of the team, and has made patently and demonstrably false allegations on front of the group and bosses about my work. It’s a small team and he’s a domineering personality and the boss doesn’t intervene. I calmly corrected his allegations in reply. Now I will not read another of his emails, for my mental health. I like that decision. I’ve worked on so very many models and coaching sessions on not giving him any power; however his behaviour meets the work safety legislation’s definition of bullying, and now his claims are next bizarre as they are factually incorrect. I can’t seem to get to a place where his behaviour doesn’t greatly upset me. I’m not sleeping, I’m in tears, I’ve been feeling depressed, scared to check my email, etc. Is there a way I can better manage my response to his behaviour? I don’t need him to like me but basic respect would be nice. I’m an email away from quitting. Which is a shame – it’s a good project. But I cannot abide by this unchallenged behaviour and maintain self respect. Is there a helpful way to work through this? I don’t want to leave but cannot see another way. Help!