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Theorem nfrab1 2831
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 2658 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
2 nfab1 2525 . 2  |-  F/_ x { x  |  (
x  e.  A  /\  ph ) }
31, 2nfcxfr 2520 1  |-  F/_ x { x  e.  A  |  ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 359    e. wcel 1717   {cab 2373   F/_wnfc 2510   {crab 2653
This theorem is referenced by:  reusv2lem4  4667  reusv2  4669  reusv6OLD  4674  rabxfrd  4684  onminsb  4719  tfis  4774  riotaxfrd  6517  oawordeulem  6733  nnawordex  6816  rankidb  7659  tskwe  7770  cardmin2  7818  cardaleph  7903  cardmin  8372  nnwos  10476  neiptopnei  17119  imasnopn  17643  imasncld  17644  imasncls  17645  blval2  18482  iundisj  19309  mbfinf  19424  rabexgfGS  23831  rabss3d  23839  iundisjf  23872  iundisjfi  23990  esumpinfval  24259  hasheuni  24271  measvuni  24362  ballotlem7  24572  ballotth  24574  sltval2  25334  nobndlem5  25374  cover2  26106  rfcnpre1  27358  rfcnpre2  27370  dvcosre  27409  stoweidlem14  27431  stoweidlem26  27443  stoweidlem31  27448  stoweidlem34  27451  stoweidlem35  27452  stoweidlem46  27463  stoweidlem50  27467  stoweidlem51  27468  stoweidlem52  27469  stoweidlem53  27470  stoweidlem54  27471  stoweidlem57  27474  stoweidlem59  27476  bnj1230  28512  bnj1476  28556  bnj1204  28719  bnj1311  28731
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-rab 2658
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