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Theorem ididg 4429
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 2069 . 2  |-  A  =  A
2 ideqg 4427 . 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 1524    e. wcel 1526   class class class wbr 3596    _I cid 3865
This theorem is referenced by:  issetid  4430  opelresiOLD  4558  opelresi  4559  fvi  5108  dfpo2  22005  deref  23127
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1446  ax-6 1447  ax-7 1448  ax-gen 1449  ax-8 1528  ax-11 1529  ax-14 1531  ax-17 1533  ax-12o 1567  ax-10 1581  ax-9 1587  ax-4 1594  ax-16 1780  ax-ext 2051  ax-sep 3711  ax-nul 3719  ax-pr 3779
This theorem depends on definitions:  df-bi 175  df-or 357  df-an 358  df-3an 898  df-ex 1451  df-sb 1741  df-eu 1963  df-mo 1964  df-clab 2057  df-cleq 2062  df-clel 2065  df-ne 2189  df-ral 2283  df-rex 2284  df-rab 2286  df-v 2482  df-dif 2801  df-un 2803  df-in 2805  df-ss 2809  df-nul 3078  df-if 3187  df-sn 3266  df-pr 3267  df-op 3269  df-br 3597  df-opab 3651  df-id 3870  df-xp 4280  df-rel 4281
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