Theorem nfrexd 2667

Description: Deduction version of nfrex 2670. (Contributed by Mario Carneiro, 14-Oct-2016.)

Hypotheses

Ref	Expression
nfrald.2	|- F/yph
nfrald.3	|- (ph -> F/_xA)
nfrald.4	|- (ph -> F/xps)

Assertion

Ref	Expression
nfrexd	|- (ph -> F/xE.y e. A ps)

Proof of Theorem nfrexd

Step	Hyp	Ref	Expression
1		dfrex2 2628	. 2 |- (E.y e. A ps <-> -. A.y e. A -. ps)
2		nfrald.2	. . . 4 |- F/yph
3		nfrald.3	. . . 4 |- (ph -> F/_xA)
4		nfrald.4	. . . . 5 |- (ph -> F/xps)
5	4	nfnd 1791	. . . 4 |- (ph -> F/x -. ps)
6	2, 3, 5	nfrald 2666	. . 3 |- (ph -> F/xA.y e. A -. ps)
7	6	nfnd 1791	. 2 |- (ph -> F/x -. A.y e. A -. ps)
8	1, 7	nfxfrd 1571	1 |- (ph -> F/xE.y e. A ps)

Syntax hints:  -. wn 3   -> wi 4   F/wnf 1544   F/_wnfc 2477  A.wral 2615  E.wrex 2616

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2479  df-ral 2620  df-rex 2621

This theorem is referenced by:  nfunid  3899