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Theorem breqtri 4237
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 4222 . 2  |-  ( A R B  <->  A R C )
41, 3mpbi 201 1  |-  A R C
Colors of variables: wff set class
Syntax hints:    = wceq 1653   class class class wbr 4214
This theorem is referenced by:  breqtrri  4239  3brtr3i  4241  supsrlem  8988  0lt1  9552  hashunlei  11686  sqr2gt1lt2  12082  trireciplem  12643  cos1bnd  12790  cos2bnd  12791  cos01gt0  12794  sin4lt0  12798  rpnnen2lem3  12818  gcdaddmlem  13030  dec2dvds  13401  abvtrivd  15930  sincos4thpi  20423  log2cnv  20786  log2ublem2  20789  log2ublem3  20790  birthday  20795  harmonicbnd3  20848  basellem7  20871  ppiublem1  20988  ppiublem2  20989  ppiub  20990  bposlem9  21078  lgsdir2lem2  21110  lgsdir2lem3  21111  ex-fl  21757  siilem1  22354  normlem5  22618  normlem6  22619  norm-ii-i  22641  norm3adifii  22652  cmm2i  23111  mayetes3i  23234  nmopcoadji  23606  mdoc2i  23931  dmdoc2i  23933  sqsscirc1  24308  log2le1  24409  ballotlemfc0  24752  ballotlemfcc  24753  ballotlem1c  24767  lgam1  24850  circum  25113  cntotbnd  26507  jm2.23  27069  stoweidlem7  27734  wallispi  27797  stirlinglem1  27801
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215
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