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Theorem eqbrtrri 4175
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtrr.1  |-  A  =  B
eqbrtrr.2  |-  A R C
Assertion
Ref Expression
eqbrtrri  |-  B R C

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3  |-  A  =  B
21eqcomi 2392 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 4173 1  |-  B R C
Colors of variables: wff set class
Syntax hints:    = wceq 1649   class class class wbr 4154
This theorem is referenced by:  3brtr3i  4181  expnass  11414  faclbnd4lem1  11512  sqr2gt1lt2  12008  cos1bnd  12716  cos2bnd  12717  prdsvalstr  13604  ovolre  19289  pige3  20293  atan1  20636  log2ublem1  20654  sqrlim  20679  bposlem8  20943  chebbnd1  21034  konigsberg  21558  norm-ii-i  22488  nmopadji  23442  unierri  23456  ballotlem2  24526  stoweidlem26  27444  wallispilem5  27487
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-rab 2659  df-v 2902  df-dif 3267  df-un 3269  df-in 3271  df-ss 3278  df-nul 3573  df-if 3684  df-sn 3764  df-pr 3765  df-op 3767  df-br 4155
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