Theorem 2nexaln

Description: Theorem *11.25 in WhiteheadRussell p. 160. (Contributed by Andrew Salmon, 24-May-2011)

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

Proof

Step	Hyp	Ref	Expression
1		2exnaln	$$⊢\exists x\exists y\phi \leftrightarrow \neg \forall x\forall y\neg \phi$$
2	1	bicomi	$$⊢\neg \forall x\forall y\neg \phi \leftrightarrow \exists x\exists y\phi$$
3	2	con1bii	$$⊢\neg \exists x\exists y\phi \leftrightarrow \forall x\forall y\neg \phi$$