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Theorem nfrmo1 2580
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 2401 . 2  |-  ( E* x  e.  A  ph  <->  E* x ( x  e.  A  /\  ph )
)
2 nfmo1 1989 . 2  |-  F/ x E* x ( x  e.  A  /\  ph )
31, 2nfxfr 1435 1  |-  F/ x E* x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 103   F/wnf 1421    e. wcel 1465   E*wmo 1978   E*wrmo 2396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-eu 1980  df-mo 1981  df-rmo 2401
This theorem is referenced by:  nfdisj1  3889
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