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Theorem nfreu1 2662
Description:  x is not free in  E! x  e.  A ph. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfreu1  |-  F/ x E! x  e.  A  ph

Proof of Theorem nfreu1
StepHypRef Expression
1 df-reu 2475 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 2049 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1485 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 104   F/wnf 1471   E!weu 2038    e. wcel 2160   E!wreu 2470
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-eu 2041  df-reu 2475
This theorem is referenced by:  riota2df  5867
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