You mean like a dependency tree? There isn’t a comprehensive one — it would be way too big and we don’t have all mathematical knowledge written down in one place anyway.
But if you’re interested in any given classical result, if you ask I’m sure a mathematician can give you a rough idea of what the path back down to first principles is. If you’re not literally interested in starting by assuming the existence of the empty set, say, then opening any introductory book on the topic will give you an idea. Just look at the proof of the result and follow its references back. It won’t go that deep.
But if you’re interested in any given classical result, if you ask I’m sure a mathematician can give you a rough idea of what the path back down to first principles is. If you’re not literally interested in starting by assuming the existence of the empty set, say, then opening any introductory book on the topic will give you an idea. Just look at the proof of the result and follow its references back. It won’t go that deep.