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Theorem ididg 4147
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 1960 . 2 |- A = A
2 ideqg 4145 . 2 |- (A e. V -> (A _I A <-> A = A))
31, 2mpbiri 243 1 |- (A e. V -> A _I A)
Colors of variables: wff set class
Syntax hints:   -> wi 4   = wceq 1457   e. wcel 1459   class class class wbr 3376   _I cid 3623
This theorem is referenced by:  opelxpex2 4148  issetid 4149  fvi 4837  dfpo2 13882  eltids 14879  deref 15133
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1376  ax-6 1377  ax-7 1378  ax-gen 1379  ax-8 1461  ax-10 1462  ax-11 1463  ax-12 1464  ax-14 1466  ax-17 1473  ax-9 1488  ax-4 1494  ax-16 1671  ax-ext 1942  ax-sep 3472  ax-nul 3481  ax-pr 3541
This theorem depends on definitions:  df-bi 190  df-or 383  df-an 384  df-ex 1381  df-sb 1633  df-eu 1860  df-mo 1861  df-clab 1948  df-cleq 1953  df-clel 1956  df-ne 2080  df-v 2367  df-dif 2665  df-un 2667  df-in 2669  df-ss 2671  df-nul 2927  df-sn 3099  df-pr 3100  df-op 3103  df-br 3377  df-opab 3431  df-id 3627  df-xp 4014  df-rel 4015
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