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Theorem nfrmo1 3001
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 2784 . 2  |-  ( E* x  e.  A  ph  <->  E* x ( x  e.  A  /\  ph )
)
2 nfmo1 2278 . 2  |-  F/ x E* x ( x  e.  A  /\  ph )
31, 2nfxfr 1693 1  |-  F/ x E* x  e.  A  ph
Colors of variables: wff setvar class
Syntax hints:    /\ wa 371   F/wnf 1664    e. wcel 1869   E*wmo 2267   E*wrmo 2779
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-ex 1661  df-nf 1665  df-eu 2270  df-mo 2271  df-rmo 2784
This theorem is referenced by:  nfdisj1  4405  2reu3  38366
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