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

Theorem eqbrtrri 4225
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtrr.1
eqbrtrr.2
Assertion
Ref Expression
eqbrtrri

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3
21eqcomi 2439 . 2
3 eqbrtrr.2 . 2
42, 3eqbrtri 4223 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   class class class wbr 4204 This theorem is referenced by:  3brtr3i  4231  expnass  11478  faclbnd4lem1  11576  sqr2gt1lt2  12072  cos1bnd  12780  cos2bnd  12781  prdsvalstr  13668  ovolre  19413  pige3  20417  atan1  20760  log2ublem1  20778  sqrlim  20803  bposlem8  21067  chebbnd1  21158  konigsberg  21701  norm-ii-i  22631  nmopadji  23585  unierri  23599  ballotlem2  24738  stoweidlem26  27742  wallispilem5  27785 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  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
 Copyright terms: Public domain W3C validator