ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfrab1 Unicode version

Theorem nfrab1 2643
Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)
Assertion
Ref Expression
nfrab1  |-  F/_ x { x  e.  A  |  ph }

Proof of Theorem nfrab1
StepHypRef Expression
1 df-rab 2451 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 nfab1 2308 . 2  |-  F/_ x { x  |  (
x  e.  A  /\  ph ) }
31, 2nfcxfr 2303 1  |-  F/_ x { x  e.  A  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    e. wcel 2135   {cab 2150   F/_wnfc 2293   {crab 2446
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 1434  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-rab 2451
This theorem is referenced by:  repizf2  4136  rabxfrd  4442  onintrab2im  4490  tfis  4555  fvmptssdm  5565  infssuzcldc  11873  nnwosdc  11961  imasnopn  12866
  Copyright terms: Public domain W3C validator