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Theorem opabresid 5178
 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 5171 . 2
2 equcom 1846 . . . . 5
32opabbii 4490 . . . 4
4 dfid3 4770 . . . 4
53, 4eqtr4i 2461 . . 3
65reseq1i 5121 . 2
71, 6eqtr3i 2460 1
 Colors of variables: wff setvar class Syntax hints:   wa 370   wceq 1437   wcel 1870  copab 4483   cid 4764   cres 4856 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-opab 4485  df-id 4769  df-xp 4860  df-rel 4861  df-res 4866 This theorem is referenced by:  mptresid  5179  pospo  16170  opsrtoslem1  18642  tgphaus  21062  relexp0eq  35932
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