MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfreu1 Unicode version

Theorem nfreu1 2723
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 2563 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 2166 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1560 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 358   F/wnf 1534    e. wcel 1696   E!weu 2156   E!wreu 2558
This theorem is referenced by:  nfriota1  6328  riota2df  6341  2reu8  28073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160  df-reu 2563
  Copyright terms: Public domain W3C validator