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Theorem brab 4775
Description: The law of concretion for a binary relation. (Contributed by NM, 16-Aug-1999.)
Hypotheses
Ref Expression
opelopab.1
opelopab.2
opelopab.3
opelopab.4
brab.5
Assertion
Ref Expression
brab
Distinct variable groups:   , ,   , ,   , ,

Proof of Theorem brab
StepHypRef Expression
1 opelopab.1 . 2
2 opelopab.2 . 2
3 opelopab.3 . . 3
4 opelopab.4 . . 3
5 brab.5 . . 3
63, 4, 5brabg 4771 . 2
71, 2, 6mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818   cvv 3109   class class class wbr 4452  {copab 4509
This theorem is referenced by:  opbrop  5084  f1oweALT  6784  frxp  6910  fnwelem  6915  dftpos4  6993  dfac3  8523  axdc2lem  8849  brdom7disj  8930  brdom6disj  8931  ordpipq  9341  ltresr  9538  shftfn  12906  2shfti  12913  ishpg  24128  brcgr  24203  ex-opab  25153  br8d  27463  br8  29185  br6  29186  br4  29187  poseq  29333  dfbigcup2  29549  brsegle  29758  heiborlem2  30308
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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