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

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

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


 * If not everything is not, there exists something that is.