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

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

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