Theorem nfexd

Description: If x is not free in ps , then it is not free in E. y ps . (Contributed by Mario Carneiro, 24-Sep-2016)

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

Proof

Step	Hyp	Ref	Expression
1		nfald.1	|- F/ y ph
2		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	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 )