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Theorem ididg 5507
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 5505 . 2 (𝐴𝑉 → (𝐴 I 𝐴𝐴 = 𝐴))
31, 2mpbiri 250 1 (𝐴𝑉𝐴 I 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1658  wcel 2166   class class class wbr 4872   I cid 5248
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2390  ax-ext 2802  ax-sep 5004  ax-nul 5012  ax-pr 5126
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-mo 2604  df-eu 2639  df-clab 2811  df-cleq 2817  df-clel 2820  df-nfc 2957  df-ral 3121  df-rex 3122  df-rab 3125  df-v 3415  df-dif 3800  df-un 3802  df-in 3804  df-ss 3811  df-nul 4144  df-if 4306  df-sn 4397  df-pr 4399  df-op 4403  df-br 4873  df-opab 4935  df-id 5249  df-xp 5347  df-rel 5348
This theorem is referenced by:  issetid  5508  opelidres  5644  fvi  6501
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