Theorem bj-nfexd

Description: Variant of nfexd . (Contributed by BJ, 25-Dec-2023)

	Ref	Expression
Hypotheses	bj-nfald.1	|- ( ph -> A. y ph )
	bj-nfald.2	|- ( ph -> F/ x ps )
Assertion	bj-nfexd	|- ( ph -> F/ x E. y ps )

Proof

Step	Hyp	Ref	Expression
1		bj-nfald.1	|- ( ph -> A. y ph )
2		bj-nfald.2	|- ( ph -> F/ x ps )
3		df-ex	|- ( E. y ps <-> -. A. y -. ps )
4	2	nfnd	|- ( ph -> F/ x -. ps )
5	1 4	bj-nfald	|- ( ph -> F/ x A. y -. ps )
6	5	nfnd	|- ( ph -> F/ x -. A. y -. ps )
7	3 6	nfxfrd	|- ( ph -> F/ x E. y ps )