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Theorem ididg 4463
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 2100 . 2  |-  A  =  A
2 ideqg 4461 . 2  |-  ( A  e.  V  ->  ( A  _I  A  <->  A  =  A ) )
31, 2mpbiri 222 1  |-  ( A  e.  V  ->  A  _I  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1531    e. wcel 1533   class class class wbr 3630    _I cid 3899
This theorem is referenced by:  issetid  4464  opelresiOLD  4592  opelresi  4593  fvi  5142  dfpo2  22040  deref  23172
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1452  ax-6 1453  ax-7 1454  ax-gen 1455  ax-8 1535  ax-11 1536  ax-14 1538  ax-17 1540  ax-12o 1574  ax-10 1588  ax-9 1594  ax-4 1601  ax-16 1787  ax-ext 2082  ax-sep 3745  ax-nul 3753  ax-pr 3813
This theorem depends on definitions:  df-bi 175  df-or 357  df-an 358  df-3an 902  df-ex 1457  df-sb 1748  df-eu 1970  df-mo 1971  df-clab 2088  df-cleq 2093  df-clel 2096  df-ne 2220  df-ral 2315  df-rex 2316  df-rab 2318  df-v 2514  df-dif 2833  df-un 2835  df-in 2837  df-ss 2841  df-nul 3111  df-if 3221  df-sn 3300  df-pr 3301  df-op 3303  df-br 3631  df-opab 3685  df-id 3904  df-xp 4314  df-rel 4315
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