Theorem bj-dvelimv

Description: A version of dvelim using the "nonfree" idiom. (Contributed by BJ, 20-Oct-2021) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-dvelimv.nf	|- F/ x ps
	bj-dvelimv.is	|- ( z = y -> ( ps <-> ph ) )
Assertion	bj-dvelimv	|- ( -. A. x x = y -> F/ x ph )

Proof

Step	Hyp	Ref	Expression
1		bj-dvelimv.nf	|- F/ x ps
2		bj-dvelimv.is	|- ( z = y -> ( ps <-> ph ) )
3	1	a1i	|- ( T. -> F/ x ps )
4	3 2	bj-dvelimdv1	|- ( T. -> ( -. A. x x = y -> F/ x ph ) )
5	4	mptru	|- ( -. A. x x = y -> F/ x ph )