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Metamath Proof Explorer

Theorem hbnaes

Description: Rule that applies hbnae to antecedent. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by NM, 15-May-1993) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	hbnaes.1	$⊢ \forall z \neg \forall x x = y \to φ$
	Assertion	hbnaes	$⊢ \neg \forall x x = y \to φ$

Proof

Step	Hyp	Ref	Expression
1		hbnaes.1	$⊢ \forall z \neg \forall x x = y \to φ$
2		hbnae	$⊢ \neg \forall x x = y \to \forall z \neg \forall x x = y$
3	2 1	syl	$⊢ \neg \forall x x = y \to φ$