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Theorem opelresi 5161
 Description: belongs to a restriction of the identity class iff belongs to the restricting class. (Contributed by FL, 27-Oct-2008.) (Revised by NM, 30-Mar-2016.)
Assertion
Ref Expression
opelresi

Proof of Theorem opelresi
StepHypRef Expression
1 opelresg 5156 . 2
2 ididg 5029 . . . 4
3 df-br 4216 . . . 4
42, 3sylib 190 . . 3
54biantrurd 496 . 2
61, 5bitr4d 249 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wcel 1726  cop 3819   class class class wbr 4215   cid 4496   cres 4883 This theorem is referenced by:  issref  5250  ustfilxp  18247  ustelimasn  18257  metustfbasOLD  18600  metustfbas  18601 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-res 4893
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