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Theorem eqbrtrri 4416
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999.)
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 2465 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 4414 1  |-  B R C
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   class class class wbr 4395
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-rab 2805  df-v 3074  df-dif 3434  df-un 3436  df-in 3438  df-ss 3445  df-nul 3741  df-if 3895  df-sn 3981  df-pr 3983  df-op 3987  df-br 4396
This theorem is referenced by:  3brtr3i  4422  expnass  12083  faclbnd4lem1  12181  sqr2gt1lt2  12877  cos1bnd  13584  cos2bnd  13585  prdsvalstr  14505  ovolre  21135  pige3  22107  atan1  22451  log2ublem1  22469  sqrlim  22494  bposlem8  22758  chebbnd1  22849  konigsberg  23755  norm-ii-i  24686  nmopadji  25641  unierri  25655  ballotlem2  27010  stoweidlem26  29964  wallispilem5  30007
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