De Morgan's Laws (Predicate Logic)/Denial of Existence

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

Then:
 * $\forall x: \neg P \left({x}\right) \dashv \vdash \neg \exists x: P \left({x}\right)$


 * If everything is not, there exists nothing that is.