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

Theorem eqbrtrri 4424
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999.)
Hypotheses
Ref Expression
eqbrtrr.1
eqbrtrr.2
Assertion
Ref Expression
eqbrtrri

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3
21eqcomi 2460 . 2
3 eqbrtrr.2 . 2
42, 3eqbrtri 4422 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1444   class class class wbr 4402 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403 This theorem is referenced by:  3brtr3i  4430  expnass  12380  faclbnd4lem1  12478  sqrt2gt1lt2  13338  cos1bnd  14241  cos2bnd  14242  2strstr1  15233  prdsvalstr  15351  ovolre  22479  pige3  23472  atan1  23854  log2ublem1  23872  sqrtlim  23898  bposlem8  24219  chebbnd1  24310  konigsberg  25715  norm-ii-i  26790  nmopadji  27743  unierri  27757  ballotlem2  29321  pigt3  31938  stoweidlem26  37886  wallispilem5  37931
 Copyright terms: Public domain W3C validator