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Theorem eqbrtrri 5080
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999.)
Hypotheses
Ref Expression
eqbrtrr.1 𝐴 = 𝐵
eqbrtrr.2 𝐴𝑅𝐶
Assertion
Ref Expression
eqbrtrri 𝐵𝑅𝐶

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3 𝐴 = 𝐵
21eqcomi 2827 . 2 𝐵 = 𝐴
3 eqbrtrr.2 . 2 𝐴𝑅𝐶
42, 3eqbrtri 5078 1 𝐵𝑅𝐶
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528   class class class wbr 5057
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-br 5058
This theorem is referenced by:  3brtr3i  5086  expnass  13558  faclbnd4lem1  13641  sqrt2gt1lt2  14622  cos1bnd  15528  cos2bnd  15529  2strstr1  16593  prdsvalstr  16714  ovolre  24053  pigt3  25030  pige3ALT  25032  atan1  25433  log2ublem1  25451  sqrtlim  25477  bposlem8  25794  chebbnd1  25975  norm-ii-i  28841  nmopadji  29794  unierri  29808  ballotlem2  31645  hgt750lemd  31818  hgt750lem  31821  stoweidlem26  42188  wallispilem5  42231
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