ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfre1 Unicode version

Theorem nfre1 2453
Description:  x is not free in  E. x  e.  A ph. (Contributed by NM, 19-Mar-1997.) (Revised by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
nfre1  |-  F/ x E. x  e.  A  ph

Proof of Theorem nfre1
StepHypRef Expression
1 df-rex 2399 . 2  |-  ( E. x  e.  A  ph  <->  E. x ( x  e.  A  /\  ph )
)
2 nfe1 1457 . 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.wex 1453    e. wcel 1465   E.wrex 2394
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-gen 1410  ax-ie1 1454
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-rex 2399
This theorem is referenced by:  r19.29an  2551  nfiu1  3813  fun11iun  5356  eusvobj2  5728  fodjuomnilemdc  6984  ismkvnex  6997  prarloclem3step  7272  prmuloc2  7343  ltexprlemm  7376  caucvgprprlemaddq  7484  caucvgsrlemgt1  7571  axpre-suploclemres  7677  supinfneg  9358  infsupneg  9359  lbzbi  9376  divalglemeunn  11545  divalglemeuneg  11547  bezoutlemmain  11613  bezout  11626  isomninnlem  13152
  Copyright terms: Public domain W3C validator