Show that if a set of sentences S entails a sentence F, then some finite subset of S implies F.

Here's what I have so far. Suppose S entails F, and for reductio, that no finite subset of S implies F. So, for every finite subset S*, there is an interpretation that makes every sentence in S* true and F false. A fortiori, this means that for every finite subset S* of S, there is an interpretation that makes every sentence in S* true. By the compactness theorem, this means that S has a model, call itM. Since S entails F, F will be true onM.

I don't know where to go from here.