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Theorem nfreu1 2999
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 2782 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 2276 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1692 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff setvar class
Syntax hints:    /\ wa 370   F/wnf 1663    e. wcel 1868   E!weu 2265   E!wreu 2777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664  df-eu 2269  df-reu 2782
This theorem is referenced by:  riota2df  6284  2reu8  38326  iccpartdisj  38463
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