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

From ProofWiki
Jump to: navigation, search

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.


Proof


Source of Name

This entry was named for Augustus De Morgan.


Sources