Existential Quantifier Distributes over Conjunction

Theorem
Let $\map \phi x, \map \psi x$ be WFFs of the free variable $x$.

Then:
 * $\exists x: \paren {\map \phi x \land \map \psi x} \vdash \paren {\exists x: \map \phi x} \land \paren {\exists x: \map \psi x}$