Theorem nfrmo1 2782

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

Assertion

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

Proof of Theorem nfrmo1

Step	Hyp	Ref	Expression
1		df-rmo 2622	. 2 |- (E*x e. A ph <-> E*x(x e. A /\ ph))
2		nfmo1 2215	. 2 |- F/xE*x(x e. A /\ ph)
3	1, 2	nfxfr 1570	1 |- F/xE*x e. A ph

Syntax hints:   /\ wa 358   F/wnf 1544   e. wcel 1710  E*wmo 2205  E*wrmo 2617

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

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209  df-rmo 2622

This theorem is referenced by: (None)