De Morgan's Laws (Predicate Logic)/Denial of Universality/Formulation 2/Reverse Implication

Theorem
Let $\forall$ and $\exists$ denote the universal quantifier and existential quantifier respectively.

Then:
 * $\vdash \paren{ \exists x: \neg \map P x } \implies \neg \paren {\forall x: \map P x}$