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Theorem ididg 4837
Description: A set is identical to itself. (Contributed by NM, 28-May-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
ididg  |-  ( A  e.  V  ->  A  _I  A )

Proof of Theorem ididg
StepHypRef Expression
1 eqid 2283 . 2  |-  A  =  A
2 ideqg 4835 . 2  |-  ( A  e.  V  ->  ( A  _I  A  <->  A  =  A ) )
31, 2mpbiri 224 1  |-  ( A  e.  V  ->  A  _I  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   class class class wbr 4023    _I cid 4304
This theorem is referenced by:  issetid  4838  opelresiOLD  4966  opelresi  4967  fvi  5579  dfpo2  24112  deref  25288
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-id 4309  df-xp 4695  df-rel 4696
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