Theorem exnal

Description: Existential quantification of negation is equivalent to negation of universal quantification. Dual of alnex . See also the dual pair df-ex / alex . Theorem 19.14 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Assertion	exnal	$$⊢\exists x\neg \phi \leftrightarrow \neg \forall x\phi$$

Proof

Step	Hyp	Ref	Expression
1		alex	$$⊢\forall x\phi \leftrightarrow \neg \exists x\neg \phi$$
2	1	con2bii	$$⊢\exists x\neg \phi \leftrightarrow \neg \forall x\phi$$