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Theorem opabresid 5332
 Description: The restricted identity expressed with the class builder. (Contributed by FL, 25-Apr-2012.)
Assertion
Ref Expression
opabresid
Distinct variable group:   ,,

Proof of Theorem opabresid
StepHypRef Expression
1 resopab 5325 . 2
2 equcom 1794 . . . . 5
32opabbii 4516 . . . 4
4 dfid3 4801 . . . 4
53, 4eqtr4i 2489 . . 3
65reseq1i 5274 . 2
71, 6eqtr3i 2488 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {copab 4509   cid 4795  |`cres 5006 This theorem is referenced by:  mptresid  5333  pospo  15603  opsrtoslem1  18148  tgphaus  20615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-res 5016
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