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Theorem rabid 2876
Description: An "identity" law of concretion for restricted abstraction. Special case of Definition 2.1 of [Quine] p. 16. (Contributed by NM, 9-Oct-2003.)
Assertion
Ref Expression
rabid  |-  ( x  e.  { x  e.  A  |  ph }  <->  ( x  e.  A  /\  ph ) )

Proof of Theorem rabid
StepHypRef Expression
1 df-rab 2706 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
21abeq2i 2542 1  |-  ( x  e.  { x  e.  A  |  ph }  <->  ( x  e.  A  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    e. wcel 1725   {crab 2701
This theorem is referenced by:  rabeq2i  2945  reusv2lem4  4718  reusv2  4720  rabxfrd  4735  tfis  4825  riotaxfrd  6572  rankr1ai  7713  cfval2  8129  cflim3  8131  cflim2  8132  cfss  8134  cfslb  8135  cofsmo  8138  nnwos  10533  ramval  13364  ramub1lem1  13382  neiptopnei  17184  hauseqlcld  17666  imasnopn  17710  imasncld  17711  imasncls  17712  ptcmplem4  18074  blval2  18593  metutopOLD  18600  psmetutop  18601  mbfinf  19545  itg2monolem1  19630  lhop1  19886  rabexgfGS  23975  rabss3d  23983  esumpinfval  24451  hasheuni  24463  measvuni  24556  elorvc  24705  ballotlemimin  24751  ballotlem7  24781  ballotth  24783  mbfposadd  26200  cover2  26352  aaitgo  27282  rfcnpre1  27604  rfcnpre2  27616  dvcosre  27655  itgsinexplem1  27662  stoweidlem27  27690  stoweidlem31  27694  stoweidlem34  27697  stoweidlem35  27698  stoweidlem59  27722  2spotmdisj  28315  bnj1204  29235
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-rab 2706
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