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Theorem ididg 5712
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 (𝐴𝑉𝐴 I 𝐴)

Proof of Theorem ididg
StepHypRef Expression
1 eqid 2824 . 2 𝐴 = 𝐴
2 ideqg 5710 . 2 (𝐴𝑉 → (𝐴 I 𝐴𝐴 = 𝐴))
31, 2mpbiri 261 1 (𝐴𝑉𝐴 I 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538  wcel 2115   class class class wbr 5053   I cid 5447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5190  ax-nul 5197  ax-pr 5318
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-v 3483  df-dif 3923  df-un 3925  df-in 3927  df-ss 3937  df-nul 4278  df-if 4452  df-sn 4552  df-pr 4554  df-op 4558  df-br 5054  df-opab 5116  df-id 5448  df-xp 5549  df-rel 5550
This theorem is referenced by:  issetid  5713  opelidres  5853  fvi  6732
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