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

< De Morgan's Laws (Predicate Logic)(Redirected from Denial of Existence)

## Contents

## 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

- 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 3.1 \ \text{(ii)}$: Statements and conditions; quantifiers - 1980: D.J. O'Connor and Betty Powell:
*Elementary Logic*... (previous) ... (next): $\S \text{III}$: The Logic of Predicates $(1): \ 3$: Quantifiers: Relations between quantifiers $2$ - 1996: H. Jerome Keisler and Joel Robbin:
*Mathematical Logic and Computability*: $\S 2.1$