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Theorem nfreu1 2577
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 2398 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 1986 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1433 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 103   F/wnf 1419    e. wcel 1463   E!weu 1975   E!wreu 2393
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 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-eu 1978  df-reu 2398
This theorem is referenced by:  riota2df  5716
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