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Theorem brabg 4771
 Description: The law of concretion for a binary relation. (Contributed by NM, 16-Aug-1999.) (Revised by Mario Carneiro, 19-Dec-2013.)
Hypotheses
Ref Expression
opelopabg.1
opelopabg.2
brabg.5
Assertion
Ref Expression
brabg
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem brabg
StepHypRef Expression
1 opelopabg.1 . . 3
2 opelopabg.2 . . 3
31, 2sylan9bb 699 . 2
4 brabg.5 . 2
53, 4brabga 4766 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818   class class class wbr 4452  {copab 4509 This theorem is referenced by:  brab  4775  ideqg  5159  opelcnvg  5187  f1owe  6249  brrpssg  6582  bren  7545  brdomg  7546  brwdom  8014  ltprord  9429  shftfib  12905  efgrelexlema  16767  isref  20010  istrkgld  23857  islnopp  24113  axcontlem5  24271  isfrgra  24990  cmbr  26502  leopg  27041  cvbr  27201  mdbr  27213  dmdbr  27218  soseq  29334  sltval  29407  isfne  30157  brabg2  30206  isriscg  30387  lcvbr  34746 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
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