Is there, or is someone creating a survey/encyclopaedia/website of mathematical theorems which connects theorems together with their assumptions (axioms, other theorems, hypotheses etc.)? I'm thinking something that could be modeled by a directed graph showing which (named/important) statements can prove other (named/important) statements.
Initial investigations: It doesn't seem that either ProofWiki or planetmath.org have this structure.
I suggest that you look at the Metamath Proof Explorer. It contains thousands of proofs written in a strictly formal style, and they are linked together so that you could hypothetically expand all subproofs and each branch would end with an axiom (of ZFC).
I think it's the closest thing to what you asked for. You need to look at proofs and not just at the statements of theorems, otherwise they would all be connected, since every provable proposition trivially implies all provable propositions.