Theorem nfrmo1 2670

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 2483	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
2		nfmo1 2057	. 2 |- F/ x E* x ( x e. A /\ ph )
3	1, 2	nfxfr 1488	1 |- F/ x E* x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1474   E*wmo 2046   e. wcel 2167   E*wrmo 2478

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-eu 2048  df-mo 2049  df-rmo 2483

This theorem is referenced by:  nfdisj1  4023