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Theorem eqbrrdiv 4974
 Description: Deduction from extensionality principle for relations. (Contributed by Rodolfo Medina, 10-Oct-2010.)
Hypotheses
Ref Expression
eqbrrdiv.1
eqbrrdiv.2
eqbrrdiv.3
Assertion
Ref Expression
eqbrrdiv
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem eqbrrdiv
StepHypRef Expression
1 eqbrrdiv.1 . 2
2 eqbrrdiv.2 . 2
3 eqbrrdiv.3 . . 3
4 df-br 4213 . . 3
5 df-br 4213 . . 3
63, 4, 53bitr3g 279 . 2
71, 2, 6eqrelrdv 4972 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  cop 3817   class class class wbr 4212   wrel 4883 This theorem is referenced by:  funcpropd  14097  fullpropd  14117  fthpropd  14118  dvres  19798 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 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885
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