Theorem 2exnexn

Description: Theorem *11.51 in WhiteheadRussell p. 164. (Contributed by Andrew Salmon, 24-May-2011) (Proof shortened by Wolf Lammen, 25-Sep-2014)

	Ref	Expression
Assertion	2exnexn	$$⊢\exists x\forall y\phi \leftrightarrow \neg \forall x\exists y\neg \phi$$

Proof

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