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Theorem ididg 4155
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 1961 . 2 |- A = A
2 ideqg 4153 . 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 3379   _I cid 3626
This theorem is referenced by:  opelxpex2 4156  issetid 4157  fvi 4848  dfpo2 14283  eltids 15280  deref 15533
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 1672  ax-ext 1943  ax-sep 3475  ax-nul 3484  ax-pr 3544
This theorem depends on definitions:  df-bi 190  df-or 383  df-an 384  df-ex 1381  df-sb 1634  df-eu 1861  df-mo 1862  df-clab 1949  df-cleq 1954  df-clel 1957  df-ne 2081  df-v 2368  df-dif 2666  df-un 2668  df-in 2670  df-ss 2672  df-nul 2928  df-sn 3102  df-pr 3103  df-op 3106  df-br 3380  df-opab 3434  df-id 3630  df-xp 4022  df-rel 4023
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