Hi all, I have to do a proof and I keep hitting dead ends.

The proof is:

"Show the following general statements are equivalent. ($\displaystyle \Gamma$ and $\displaystyle \Sigma$ are sets of formulas and $\displaystyle \phi$ is a formula.)

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

(F) For all $\displaystyle \Sigma$ and $\displaystyle \phi$, if $\displaystyle \Sigma\models \phi$ then $\displaystyle \Delta\models\phi$, for some finite subset $\displaystyle \Delta$ of $\displaystyle \Sigma$."

I want to prove (E) --> (F) and then (F) --> (E), but I feel like I keep proving the converse of what I want to prove.

I thought I could try using the contrapositives of these statements, or try a proof by contradiction, but nothing seems to be working in the right direction.