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Theorem ididg 4436
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 2082 . 2  |-  A  =  A
2 ideqg 4434 . 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 1536    e. wcel 1538   class class class wbr 3600    _I cid 3869
This theorem is referenced by:  issetid  4437  fvi  5094  dfpo2  20700  eltids  21602  deref  21833
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1451  ax-6 1452  ax-7 1453  ax-gen 1454  ax-8 1540  ax-11 1541  ax-14 1543  ax-17 1545  ax-12o 1578  ax-10 1592  ax-9 1598  ax-4 1606  ax-16 1793  ax-ext 2064  ax-sep 3715  ax-nul 3723  ax-pr 3783
This theorem depends on definitions:  df-bi 175  df-or 358  df-an 359  df-3an 905  df-ex 1456  df-sb 1754  df-eu 1976  df-mo 1977  df-clab 2070  df-cleq 2075  df-clel 2078  df-ne 2201  df-ral 2295  df-rex 2296  df-rab 2298  df-v 2494  df-dif 2813  df-un 2815  df-in 2817  df-ss 2821  df-nul 3089  df-if 3199  df-sn 3278  df-pr 3279  df-op 3281  df-br 3601  df-opab 3655  df-id 3874  df-xp 4289  df-rel 4290
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