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Theorem ididg 4151
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 1953 . 2 |- A = A
2 ideqg 4149 . 2 |- (A e. V -> (A _I A <-> A = A))
31, 2mpbiri 238 1 |- (A e. V -> A _I A)
Colors of variables: wff set class
Syntax hints:   -> wi 4   = wceq 1449   e. wcel 1451   class class class wbr 3373   _I cid 3620
This theorem is referenced by:  opelxpex2 4152  issetid 4153  fvi 4844  dfpo2 14480  eltids 15477  deref 15730
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1367  ax-6 1368  ax-7 1369  ax-gen 1370  ax-8 1453  ax-10 1454  ax-11 1455  ax-12 1456  ax-14 1458  ax-17 1465  ax-9 1480  ax-4 1486  ax-16 1664  ax-ext 1935  ax-sep 3469  ax-nul 3478  ax-pr 3538
This theorem depends on definitions:  df-bi 185  df-or 378  df-an 379  df-ex 1372  df-sb 1626  df-eu 1853  df-mo 1854  df-clab 1941  df-cleq 1946  df-clel 1949  df-ne 2073  df-v 2360  df-dif 2660  df-un 2662  df-in 2664  df-ss 2666  df-nul 2922  df-sn 3096  df-pr 3097  df-op 3100  df-br 3374  df-opab 3428  df-id 3624  df-xp 4018  df-rel 4019
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