Theorem nfrexd

Description: Deduction version of nfrex . Usage of this theorem is discouraged because it depends on ax-13 . See nfrexdw for a version with a disjoint variable condition, but not requiring ax-13 . (Contributed by Mario Carneiro, 14-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfrald.1	|- F/ y ph
	nfrald.2	|- ( ph -> F/_ x A )
	nfrald.3	|- ( ph -> F/ x ps )
Assertion	nfrexd	|- ( ph -> F/ x E. y e. A ps )

Proof

Step	Hyp	Ref	Expression
1		nfrald.1	|- F/ y ph
2		nfrald.2	|- ( ph -> F/_ x A )
3		nfrald.3	|- ( ph -> F/ x ps )
4		dfrex2	|- ( E. y e. A ps <-> -. A. y e. A -. ps )
5	3	nfnd	|- ( ph -> F/ x -. ps )
6	1 2 5	nfrald	|- ( ph -> F/ x A. y e. A -. ps )
7	6	nfnd	|- ( ph -> F/ x -. A. y e. A -. ps )
8	4 7	nfxfrd	|- ( ph -> F/ x E. y e. A ps )