Not necessarily. The proof presented depends Schanuel's conjecture, but there may be another proof that doesn't depend on that conjecture, directly or indirectl

Not necessarily. The proof presented depends Schanuel's conjecture, but there may be another proof that doesn't depend on that conjecture, directly or indirectly. The question you're asking is one of metalogic. It's like asking, what is the necessary structure of the proof of some proposition? Mathematicians definitely ask questions like that, but those are tough nuts to crack.