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Theorem opelco2g 5175
Description: Ordered pair membership in a composition. (Contributed by NM, 27-Jan-1997.) (Revised by Mario Carneiro, 24-Feb-2015.)
Assertion
Ref Expression
opelco2g
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem opelco2g
StepHypRef Expression
1 brcog 5174 . 2
2 df-br 4453 . 2
3 df-br 4453 . . . 4
4 df-br 4453 . . . 4
53, 4anbi12i 697 . . 3
65exbii 1667 . 2
71, 2, 63bitr3g 287 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  <.cop 4035   class class class wbr 4452  o.ccom 5008
This theorem is referenced by:  dfco2  5511  dmfco  5947
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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  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-br 4453  df-opab 4511  df-co 5013
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