So I was thinking if I first renamed the symbols so they were consistent to make it easier for myself to think about it:

(E) For all , if every finite subset of is satisfiable, then so is .

(F) For all and , if then , for some finite subset of .

Then I could try something like, for (E)-->(F),

Try to prove the contrapositive of (F), so assume (E) and that for a \Delta \subset \Sigma, \Delta does not \models \phi. This means that \Delta is not satisfiable for any \phi, so by (E)... I'm not sure here actually, it seems like I need the converse or something.