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Theorem ididg 4143
Description: A set is identical to itself. (The proof was 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 1938 . 2 |- A = A
2 ideqg 4141 . 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 4   = wceq 1434   e. wcel 1436   class class class wbr 3363   _I cid 3612
This theorem is referenced by:  opelxpex2 4144  issetid 4145  fvi 4840  dfpo2 14694  eltids 15691  deref 15939
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1351  ax-6 1352  ax-7 1353  ax-gen 1354  ax-8 1438  ax-10 1439  ax-11 1440  ax-12 1441  ax-14 1443  ax-17 1450  ax-9 1465  ax-4 1471  ax-16 1649  ax-ext 1920  ax-sep 3459  ax-nul 3468  ax-pr 3528
This theorem depends on definitions:  df-bi 175  df-or 362  df-an 363  df-ex 1356  df-sb 1611  df-eu 1838  df-mo 1839  df-clab 1926  df-cleq 1931  df-clel 1934  df-ne 2058  df-v 2345  df-dif 2645  df-un 2647  df-in 2649  df-ss 2651  df-nul 2907  df-sn 3085  df-pr 3086  df-op 3088  df-br 3364  df-opab 3418  df-id 3616  df-xp 4010  df-rel 4011
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