Theorem nfrmo1 2681

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 2494	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
2		nfmo1 2067	. 2 |- F/ x E* x ( x e. A /\ ph )
3	1, 2	nfxfr 1498	1 |- F/ x E* x e. A ph

Syntax hints:   /\ wa 104   F/wnf 1484   E*wmo 2056   e. wcel 2178   E*wrmo 2489

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-eu 2058  df-mo 2059  df-rmo 2494

This theorem is referenced by:  nfdisj1  4048