Prove $\vdash(A\supset B)\supset C\equiv C\overline{\vee }[A\wedge \neg(B\vee C)]$ using your favorite method

Question

I've been playing with Boolean logic vs ordinary laws of logic like DeMorgan's etc., and I've come up with the following theorem in about 4 lines: $$[(A\supset B)\supset C]\equiv \left\{C\overline{\vee }[A\wedge {\sim}(B\vee C)]\right\}$$ so I was wondering if there exists a simple proof in terms of ordinary logical laws. The $\overline{\vee}$ is an exclusive or. Pretty much, this is a question of the efficiency of one kind of way of dealing with propositional logic over another.