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	$$⊢Ⅎx\phi$$
	dvelimnf.2	$$⊢z=y\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	dvelimnf	$$⊢\neg \forall xx=y\to Ⅎx\psi$$

Proof

Step	Hyp	Ref	Expression
1		dvelimnf.1	$$⊢Ⅎx\phi$$
2		dvelimnf.2	$$⊢z=y\to \left(\phi \leftrightarrow \psi \right)$$
3		nfv	$$⊢Ⅎz\psi$$
4	1 3 2	dvelimf	$$⊢\neg \forall xx=y\to Ⅎx\psi$$