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Metamath Proof Explorer

Theorem nfnaew

Description: All variables are effectively bound in a distinct variable specifier. Version of nfnae with a disjoint variable condition, which does not require ax-13 . (Contributed by Mario Carneiro, 11-Aug-2016) Avoid ax-13 . (Revised by GG, 10-Jan-2024) (Proof shortened by Wolf Lammen, 25-Sep-2024)

		Ref	Expression
	Assertion	nfnaew	$⊢ Ⅎ z \neg \forall x x = y$

Proof

Step	Hyp	Ref	Expression
1		hbnaev	$⊢ \neg \forall x x = y \to \forall z \neg \forall x x = y$
2	1	nf5i	$⊢ Ⅎ z \neg \forall x x = y$