Well, it's a proof as long as you stipulate somewhere that all the logical connectives are "if and only if." This doesn't mean that a student who writes down a long series of equations beginning with some identity to be proven and ending with some known fact has proven the identity.
Sure, that's fine, but to say that it is an invalid method of proof is wrong.
If I want to prove A, and I prove A <=> B for some proven statement B, then I have proven A! There is no question! Feels like crazy pills to think otherwise. This is a kind of backwards reasoning!
It is a kind of backwards reasoning that students empirically screw up all the time.
Edit: so much so, that I would definitely recommend students rewrite these proofs on assignments as an exerecise to make sure it's correct. By the time they reach a math PhD they probably don't need to do that anyomre. :)
