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Metamath Proof Explorer

Theorem 2exnaln

Description: Theorem *11.22 in WhiteheadRussell p. 160. (Contributed by Andrew Salmon, 24-May-2011)

		Ref	Expression
	Assertion	2exnaln	$⊢ \exists x \exists y φ \leftrightarrow \neg \forall x \forall y \neg φ$

Step	Hyp	Ref	Expression
1		df-ex	$⊢ \exists x \exists y φ \leftrightarrow \neg \forall x \neg \exists y φ$
2		alnex	$⊢ \forall y \neg φ \leftrightarrow \neg \exists y φ$
3	2	albii	$⊢ \forall x \forall y \neg φ \leftrightarrow \forall x \neg \exists y φ$
4	1 3	xchbinxr	$⊢ \exists x \exists y φ \leftrightarrow \neg \forall x \forall y \neg φ$