$(A \lor B) \to C$ and $(A \to C) \lor (B \to C)$ Which one entails the other? For a homework assignment I have to prove that one of the statements entails the other. 
The statements are:
$(A \lor B) \to C$
$(A \to C) \lor (B \to C)$
The only thing that I got so far is either $\lnot(A \lor B) \to C$ or $(A \to C) \land (B \to C)$.
I can use the rules of Modus Ponens, Modus Tollens, Simplification, Conjunction, Disjunction, Conjunctive and Disjunctive Syllogism, Hypothethical Syllogism and Conditional Proof.
The equivalence rules I can use are Double Negation, De Morgan's Laws, Biconditional Equivalence,and I think, Transposition and Material Implication, too. 
Is there someone who can help me? I've tried so much already...

Edit:
The answer they wanted to hear was:


*

*(A v B) -> C  

*A supp/CP  

*A v B disj  

*C 1,3MP  

*A -> C 2-4 CP

*(A -> C) v (B -> C)  5 disj


HINT: Use the fact that $p\to q$ is equivalent to $\neg p\lor q$. Thus,
$$(A\lor B)\to C)\equiv\neg(A\lor B)\lor C\equiv(\neg A\land\neg B)\lor C\equiv(\neg A\lor C)\land(\neg B\lor C)\;,$$
where I’ve also used De Morgan’s law and distributivity. Now expand use the same fact to convert this to an expression involving $A\to C$ and $B\to C$, and compare that with $(A\to C)\lor(B\to C)$; one of the two expressions is easily shown to imply the other.
