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Theorem ididg 4425
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 2065 . 2  |-  A  =  A
2 ideqg 4423 . 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 1520    e. wcel 1522   class class class wbr 3592    _I cid 3861
This theorem is referenced by:  issetid  4426  opelresiOLD  4554  opelresi  4555  fvi  5104  dfpo2  22001  deref  23122
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1442  ax-6 1443  ax-7 1444  ax-gen 1445  ax-8 1524  ax-11 1525  ax-14 1527  ax-17 1529  ax-12o 1563  ax-10 1577  ax-9 1583  ax-4 1590  ax-16 1776  ax-ext 2047  ax-sep 3707  ax-nul 3715  ax-pr 3775
This theorem depends on definitions:  df-bi 175  df-or 357  df-an 358  df-3an 898  df-ex 1447  df-sb 1737  df-eu 1959  df-mo 1960  df-clab 2053  df-cleq 2058  df-clel 2061  df-ne 2185  df-ral 2279  df-rex 2280  df-rab 2282  df-v 2478  df-dif 2797  df-un 2799  df-in 2801  df-ss 2805  df-nul 3074  df-if 3183  df-sn 3262  df-pr 3263  df-op 3265  df-br 3593  df-opab 3647  df-id 3866  df-xp 4276  df-rel 4277
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