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Theorem nfrmo1 3033
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
StepHypRef Expression
1 df-rmo 2822 . 2  |-  ( E* x  e.  A  ph  <->  E* x ( x  e.  A  /\  ph )
)
2 nfmo1 2289 . 2  |-  F/ x E* x ( x  e.  A  /\  ph )
31, 2nfxfr 1625 1  |-  F/ x E* x  e.  A  ph
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369   F/wnf 1599    e. wcel 1767   E*wmo 2276   E*wrmo 2817
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-ex 1597  df-nf 1600  df-eu 2279  df-mo 2280  df-rmo 2822
This theorem is referenced by:  nfdisj1  4430  2reu3  31688
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