Use the Compactness Theorem to show: if $T \models \varphi$ then there is a finite subtheory $T' \subset T$ such that $T' \models \varphi$.
I don't see how I can use the compactness theorem here. Particularly, since the proposition seems to be some kind of weak reverse implication. Apparently the general compactness theorem goes both ways meaning: A theory $T$ is consistent if and only if every finite subtheory $T' \subset T$ is consistent. However I only know a version with just one implication: If every finite $T' \subset T$ is consistent, then so is $T$.