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

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Theorem

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

Then:

$\forall x: \neg P \paren x \dashv \vdash \neg \exists x: P \paren x$
If everything is not, there exists nothing that is.


Proof


Source of Name

This entry was named for Augustus De Morgan.


Sources