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I've been reading Enderton's Mathematical Introduction to Logic. One of the exercises on Compactness theorem requires the proof that the following corollary

[(Corollary 17A) Suppose $\Sigma \models \tau$, then there is a finite $\Sigma_0 \subseteq \Sigma$ such that $\Sigma_0 \models \tau$. ]

is equivalent to Compactness Theorem.

Can any one give me a hint on how to prove CT from this statement?

Thanks.

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    Look at Enderton's proof of the corollary for the propositional case. That will give you some ideas. Hopefully that's in your edition; I'm looking at the old one.2011-04-28

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HINT $\ (\Rightarrow)\ $ Apply CT to $\Sigma \cup \{\lnot \:\tau\}\:.\: $ $\rm\ (\Leftarrow)\ $ Let $\rm\:\tau\ =\ \exists x\ (x \ne x)$