ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfreu1 Unicode version

Theorem nfreu1 2579
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 2400 . 2  |-  ( E! x  e.  A  ph  <->  E! x ( x  e.  A  /\  ph )
)
2 nfeu1 1988 . 2  |-  F/ x E! x ( x  e.  A  /\  ph )
31, 2nfxfr 1435 1  |-  F/ x E! x  e.  A  ph
Colors of variables: wff set class
Syntax hints:    /\ wa 103   F/wnf 1421    e. wcel 1465   E!weu 1977   E!wreu 2395
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-eu 1980  df-reu 2400
This theorem is referenced by:  riota2df  5718
  Copyright terms: Public domain W3C validator