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Theorem ididg 4416
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 2061 . 2  |-  A  =  A
2 ideqg 4414 . 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 1517    e. wcel 1519   class class class wbr 3583    _I cid 3852
This theorem is referenced by:  issetid  4417  opelresiOLD  4545  opelresi  4546  fvi  5093  dfpo2  21051  deref  22175
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1439  ax-6 1440  ax-7 1441  ax-gen 1442  ax-8 1521  ax-11 1522  ax-14 1524  ax-17 1526  ax-12o 1559  ax-10 1573  ax-9 1579  ax-4 1586  ax-16 1772  ax-ext 2043  ax-sep 3698  ax-nul 3706  ax-pr 3766
This theorem depends on definitions:  df-bi 175  df-or 357  df-an 358  df-3an 895  df-ex 1444  df-sb 1733  df-eu 1955  df-mo 1956  df-clab 2049  df-cleq 2054  df-clel 2057  df-ne 2181  df-ral 2275  df-rex 2276  df-rab 2278  df-v 2474  df-dif 2793  df-un 2795  df-in 2797  df-ss 2801  df-nul 3070  df-if 3179  df-sn 3258  df-pr 3259  df-op 3261  df-br 3584  df-opab 3638  df-id 3857  df-xp 4267  df-rel 4268
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