Theorem nfrmo1 2642

Description: x is not free in E* x e. A ph. (Contributed by NM, 16-Jun-2017.)

Assertion

Ref	Expression
nfrmo1	|- F/ x E* x e. A ph

Proof of Theorem nfrmo1

Step	Hyp	Ref	Expression
1		df-rmo 2456	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
2		nfmo1 2031	. 2 |- F/ x E* x ( x e. A /\ ph )
3	1, 2	nfxfr 1467	1 |- F/ x E* x e. A ph

Syntax hints:   /\ wa 103   F/wnf 1453   E*wmo 2020   e. wcel 2141   E*wrmo 2451

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-eu 2022  df-mo 2023  df-rmo 2456

This theorem is referenced by:  nfdisj1  3979