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Theorem brco 4534
 Description: Binary relation on a composition. (Contributed by NM, 21-Sep-2004.) (Revised by Mario Carneiro, 24-Feb-2015.)
Hypotheses
Ref Expression
opelco.1
opelco.2
Assertion
Ref Expression
brco
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem brco
StepHypRef Expression
1 opelco.1 . 2
2 opelco.2 . 2
3 brcog 4530 . 2
41, 2, 3mp2an 417 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103  wex 1422   wcel 1434  cvv 2602   class class class wbr 3793   ccom 4375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-co 4380 This theorem is referenced by:  opelco  4535  cnvco  4548  resco  4855  imaco  4856  rnco  4857  coass  4869  f1eqcocnv  5462
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