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Theorem ididg 4741
 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

Proof of Theorem ididg
StepHypRef Expression
1 eqid 2253 . 2
2 ideqg 4739 . 2
31, 2mpbiri 226 1
 Colors of variables: wff set class Syntax hints:   wi 6   wceq 1619   wcel 1621   class class class wbr 3917   cid 4194 This theorem is referenced by:  issetid  4742  opelresiOLD  4870  opelresi  4871  fvi  5428  dfpo2  23213  deref  24385 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4035  ax-nul 4043  ax-pr 4105 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2511  df-rex 2512  df-rab 2514  df-v 2727  df-dif 3078  df-un 3080  df-in 3082  df-ss 3086  df-nul 3360  df-if 3468  df-sn 3547  df-pr 3548  df-op 3550  df-br 3918  df-opab 3972  df-id 4199  df-xp 4591  df-rel 4592
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