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	|- F/ x ph
	dvelimnf.2	|- ( z = y -> ( ph <-> ps ) )
Assertion	dvelimnf	|- ( -. A. x x = y -> F/ x ps )

Proof

Step	Hyp	Ref	Expression
1		dvelimnf.1	|- F/ x ph
2		dvelimnf.2	|- ( z = y -> ( ph <-> ps ) )
3		nfv	|- F/ z ps
4	1 3 2	dvelimf	|- ( -. A. x x = y -> F/ x ps )