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Theorem ididg 4723
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 2241 . 2  |-  A  =  A
2 ideqg 4721 . 2  |-  ( A  e.  V  ->  ( A  _I  A  <->  A  =  A ) )
31, 2mpbiri 223 1  |-  ( A  e.  V  ->  A  _I  A )
Colors of variables: wff set class
Syntax hints:    -> wi 5    = wceq 1608    e. wcel 1610   class class class wbr 3900    _I cid 4176
This theorem is referenced by:  issetid  4724  opelresiOLD  4852  opelresi  4853  fvi  5406  dfpo2  23088  deref  24260
This theorem was proved from axioms:  ax-1 6  ax-2 7  ax-3 8  ax-mp 9  ax-5 1522  ax-6 1523  ax-7 1524  ax-gen 1525  ax-8 1612  ax-11 1613  ax-14 1615  ax-17 1617  ax-12o 1653  ax-10 1667  ax-9 1673  ax-4 1681  ax-16 1915  ax-ext 2222  ax-sep 4017  ax-nul 4025  ax-pr 4087
This theorem depends on definitions:  df-bi 176  df-or 358  df-an 359  df-3an 935  df-tru 1309  df-ex 1527  df-nf 1529  df-sb 1872  df-eu 2106  df-mo 2107  df-clab 2228  df-cleq 2234  df-clel 2237  df-nfc 2362  df-ne 2402  df-ral 2499  df-rex 2500  df-rab 2502  df-v 2714  df-dif 3061  df-un 3063  df-in 3065  df-ss 3069  df-nul 3343  df-if 3451  df-sn 3530  df-pr 3531  df-op 3533  df-br 3901  df-opab 3955  df-id 4181  df-xp 4573  df-rel 4574
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