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Theorem ididg 4194
Description: A set is identical to itself. (The proof was shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
ididg

Proof of Theorem ididg
StepHypRef Expression
1 eqid 1918 . 2
2 ideqg 4192 . 2
31, 2mpbiri 222 1
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1414   wcel 1416   class class class wbr 3396   cid 3645
This theorem is referenced by:  issetid 4195  fvi 4932  dfpo2 17041  eltids 18036  deref 18285
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1331  ax-6 1332  ax-7 1333  ax-gen 1334  ax-8 1418  ax-10 1419  ax-11 1420  ax-12 1421  ax-14 1423  ax-17 1430  ax-9 1445  ax-4 1451  ax-16 1629  ax-ext 1900  ax-sep 3491  ax-nul 3500  ax-pr 3560
This theorem depends on definitions:  df-bi 175  df-or 358  df-an 359  df-3an 901  df-ex 1336  df-sb 1591  df-eu 1818  df-mo 1819  df-clab 1906  df-cleq 1911  df-clel 1914  df-ne 2037  df-ral 2131  df-rex 2132  df-rab 2134  df-v 2329  df-dif 2640  df-un 2642  df-in 2644  df-ss 2648  df-nul 2908  df-if 3015  df-sn 3092  df-pr 3093  df-op 3095  df-br 3397  df-opab 3450  df-id 3650  df-xp 4048  df-rel 4049
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