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Theorem brab 4287
 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:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

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 4284 . 2
71, 2, 6mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wceq 1623   wcel 1684  cvv 2788   class class class wbr 4023  copab 4076 This theorem is referenced by:  opbrop  4767  f1oweALT  5851  frxp  6225  fnwelem  6230  dftpos4  6253  dfac3  7748  axdc2lem  8074  brdom7disj  8156  brdom6disj  8157  ordpipq  8566  ltresr  8762  shftfn  11568  2shfti  11575  ex-opab  20819  br8  24113  br6  24114  br4  24115  poseq  24253  dfbigcup2  24439  brcgr  24528  brsegle  24731  inposetlem  25276  bosser  26167  heiborlem2  26536 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078
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