MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eqbrriv Unicode version

Theorem eqbrriv 5103
Description: Inference from extensionality principle for relations. (Contributed by NM, 12-Dec-2006.)
Hypotheses
Ref Expression
eqbrriv.1
eqbrriv.2
eqbrriv.3
Assertion
Ref Expression
eqbrriv
Distinct variable groups:   , ,   , ,

Proof of Theorem eqbrriv
StepHypRef Expression
1 eqbrriv.1 . 2
2 eqbrriv.2 . 2
3 eqbrriv.3 . . 3
4 df-br 4453 . . 3
5 df-br 4453 . . 3
63, 4, 53bitr3i 275 . 2
71, 2, 6eqrelriiv 5102 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  =wceq 1395  e.wcel 1818  <.cop 4035   class class class wbr 4452  Relwrel 5009
This theorem is referenced by:  resco  5516  tpostpos  6994  sbthcl  7659  dfle2  11382  dflt2  11383  idsset  29540  dfbigcup2  29549  imageval  29580
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  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  df-xp 5010  df-rel 5011
  Copyright terms: Public domain W3C validator