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Theorem breqtri 4046
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtr.1  |-  A R B
breqtr.2  |-  B  =  C
Assertion
Ref Expression
breqtri  |-  A R C

Proof of Theorem breqtri
StepHypRef Expression
1 breqtr.1 . 2  |-  A R B
2 breqtr.2 . . 3  |-  B  =  C
32breq2i 4031 . 2  |-  ( A R B  <->  A R C )
41, 3mpbi 199 1  |-  A R C
Colors of variables: wff set class
Syntax hints:    = wceq 1623   class class class wbr 4023
This theorem is referenced by:  breqtrri  4048  3brtr3i  4050  supsrlem  8733  0lt1  9296  hashunlei  11377  sqr2gt1lt2  11760  trireciplem  12320  cos1bnd  12467  cos2bnd  12468  cos01gt0  12471  sin4lt0  12475  rpnnen2lem3  12495  gcdaddmlem  12707  dec2dvds  13078  abvtrivd  15605  sincos4thpi  19881  log2cnv  20240  log2ublem2  20243  log2ublem3  20244  birthday  20249  harmonicbnd3  20301  basellem7  20324  ppiublem1  20441  ppiublem2  20442  ppiub  20443  bposlem9  20531  lgsdir2lem2  20563  lgsdir2lem3  20564  ex-fl  20834  siilem1  21429  normlem5  21693  normlem6  21694  norm-ii-i  21716  norm3adifii  21727  cmm2i  22186  mayetes3i  22309  nmopcoadji  22681  mdoc2i  23006  dmdoc2i  23008  ballotlemfc0  23051  ballotlemfcc  23052  sqsscirc1  23292  log2le1  23409  circum  24007  cntotbnd  26520  jm2.23  27089  stoweidlem7  27756  wallispi  27819  stirlinglem1  27823
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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