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Theorem eqbrtrri 4468
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 2480 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 4466 1  |-  B R C
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379   class class class wbr 4447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-br 4448
This theorem is referenced by:  3brtr3i  4474  expnass  12235  faclbnd4lem1  12333  sqrt2gt1lt2  13065  cos1bnd  13776  cos2bnd  13777  prdsvalstr  14701  ovolre  21668  pige3  22640  atan1  22984  log2ublem1  23002  sqrtlim  23027  bposlem8  23291  chebbnd1  23382  konigsberg  24660  norm-ii-i  25727  nmopadji  26682  unierri  26696  ballotlem2  28064  stoweidlem26  31326  wallispilem5  31369
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