Consistent Set of Logical Formulas is Subset of Maximally Consistent Set

Theorem
Let $\LL$ be a formal language used in the field of symbolic logic.

Let $\FF$ be the set of logical formulas of $\LL$.

Let $\FF$ be countable.

Let $S$ be a consistent subset of $\FF$.

Then $S$ is a subset of some maximal consistent set of formulas.