Theorem nfmod2 2217

Description: Bound-variable hypothesis builder for uniqueness. (Contributed by Mario Carneiro, 14-Nov-2016.)

Hypotheses

Ref	Expression
nfeud2.1	|- F/yph
nfeud2.2	|- ((ph /\ -. A.x x = y) -> F/xps)

Assertion

Ref	Expression
nfmod2	|- (ph -> F/xE*yps)

Proof of Theorem nfmod2

Step	Hyp	Ref	Expression
1		df-mo 2209	. 2 |- (E*yps <-> (E.yps -> E!yps))
2		nfeud2.1	. . . 4 |- F/yph
3		nfeud2.2	. . . 4 |- ((ph /\ -. A.x x = y) -> F/xps)
4	2, 3	nfexd2 1973	. . 3 |- (ph -> F/xE.yps)
5	2, 3	nfeud2 2216	. . 3 |- (ph -> F/xE!yps)
6	4, 5	nfimd 1808	. 2 |- (ph -> F/x(E.yps -> E!yps))
7	1, 6	nfxfrd 1571	1 |- (ph -> F/xE*yps)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358  A.wal 1540  E.wex 1541   F/wnf 1544  E!weu 2204  E*wmo 2205

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

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209

This theorem is referenced by:  nfmod  2219  nfrmod  2784  nfrmo  2786