Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  eqbrrdiv Unicode version

Theorem eqbrrdiv 4677
 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 3962 . . 3
5 df-br 3962 . . 3
63, 4, 53bitr3g 221 . 2
71, 2, 6eqrelrdv 4675 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1332   wcel 2125  cop 3559   class class class wbr 3961   wrel 4584 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-14 2128  ax-ext 2136  ax-sep 4078  ax-pow 4130  ax-pr 4164 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-v 2711  df-un 3102  df-in 3104  df-ss 3111  df-pw 3541  df-sn 3562  df-pr 3563  df-op 3565  df-br 3962  df-opab 4022  df-xp 4585  df-rel 4586 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator