Finitely Satisfiable Theory has Maximal Finitely Satisfiable Extension

Theorem
Let $T$ be a finitely satisfiable $\mathcal L$-theory.

Then there exists a finitely satisfiable $\mathcal L$-theory $T'$ which contains $T$ as a subset such that:
 * for all $\mathcal L$-sentences $\phi$, either $\phi \in T'$ or $\neg \phi \in T'$.