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Metamath Proof Explorer

Theorem dvelimnf

Description: Version of dvelim using "not free" notation. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by Mario Carneiro, 9-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	dvelimnf.1	$⊢ Ⅎ x φ$
	dvelimnf.2	$⊢ z = y \to (φ \leftrightarrow ψ)$
Assertion	dvelimnf	$⊢ \neg \forall x x = y \to Ⅎ x ψ$

Proof

Step	Hyp	Ref	Expression
1		dvelimnf.1	$⊢ Ⅎ x φ$
2		dvelimnf.2	$⊢ z = y \to (φ \leftrightarrow ψ)$
3		nfv	$⊢ Ⅎ z ψ$
4	1 3 2	dvelimf	$⊢ \neg \forall x x = y \to Ⅎ x ψ$