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Theorem rabid 2684
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 2523 . 2  |-  { x  e.  A  |  ph }  =  { x  |  ( x  e.  A  /\  ph ) }
21abeq2i 2363 1  |-  ( x  e.  { x  e.  A  |  ph }  <->  ( x  e.  A  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360    e. wcel 1621   {crab 2519
This theorem is referenced by:  rabeq2i  2737  reusv2lem4  4475  reusv2  4477  rabxfrd  4492  tfis  4582  riotaxfrd  6269  rankr1ai  7403  cfval2  7819  cflim3  7821  cflim2  7822  cfss  7824  cfslb  7825  cofsmo  7828  nnwos  10218  ramval  12982  ramub1lem1  13000  hauseqlcld  17267  ptcmplem4  17676  mbfinf  18947  itg2monolem1  19032  lhop1  19288  ballotlem2  22973  ballotlemimin  22990  ballotlem7  23020  ballotth  23022  sgplpte21a  25465  cover2  25690  aaitgo  26699  rfcnpre1  27023  rfcnpre2  27035  stoweidlem24  27073  stoweidlem27  27076  stoweidlem31  27080  stoweidlem34  27083  stoweidlem35  27084  stoweidlem54  27103  stoweidlem57  27106  stoweidlem59  27108  bnj1204  28054
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-12o 1664  ax-9 1684  ax-4 1692  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-rab 2523
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