Stuck on this propositional logic problem

Question

So I previously asked for help a couple hours ago and decided to tackle on this problem:

(A ∨ B) ∧ (A→C) ∧ (B→C)→C

I'm stuck; this is what I have so far:

1. A ∨ B (hypothesis)
2. A→C (hypothesis)
3. B→C (hypothesis)
4. A'∨C (2, implication)
5. B'∨C (3, implication)

and then I don't know what to do/prove next. Am I on the right track at least?

Answer 1

Notice that: $$ (A' \lor C) \land (B' \lor C) \equiv (A' \land B') \lor C \equiv (A \lor B)' \lor C $$