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Theorem nfreu1 3014
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 2800 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 2280 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1632 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369   F/wnf 1603    e. wcel 1804   E!weu 2268   E!wreu 2795
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840
This theorem depends on definitions:  df-bi 185  df-ex 1600  df-nf 1604  df-eu 2272  df-reu 2800
This theorem is referenced by:  riota2df  6263  2reu8  32035
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