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Theorem brab 4469
 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 4466 . 2
71, 2, 6mp2an 654 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  cvv 2948   class class class wbr 4204  copab 4257 This theorem is referenced by:  opbrop  4947  f1oweALT  6066  frxp  6448  fnwelem  6453  dftpos4  6490  dfac3  7994  axdc2lem  8320  brdom7disj  8401  brdom6disj  8402  ordpipq  8811  ltresr  9007  shftfn  11880  2shfti  11887  ex-opab  21732  br8  25371  br6  25372  br4  25373  poseq  25520  dfbigcup2  25736  brcgr  25831  brsegle  26034  heiborlem2  26512 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259
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