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Theorem eqbrtrri 4044
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 2287 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 4042 1  |-  B R C
Colors of variables: wff set class
Syntax hints:    = wceq 1623   class class class wbr 4023
This theorem is referenced by:  3brtr3i  4050  expnass  11208  faclbnd4lem1  11306  sqr2gt1lt2  11760  cos1bnd  12467  cos2bnd  12468  prdsvalstr  13353  ovolre  18884  pige3  19885  atan1  20224  log2ublem1  20242  sqrlim  20267  bposlem8  20530  chebbnd1  20621  norm-ii-i  21716  nmopadji  22670  unierri  22684  konigsberg  23911  stoweidlem26  27775  wallispilem5  27818
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024
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