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Theorem eqbrtri 4026
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtr.1 𝐴 = 𝐵
eqbrtr.2 𝐵𝑅𝐶
Assertion
Ref Expression
eqbrtri 𝐴𝑅𝐶

Proof of Theorem eqbrtri
StepHypRef Expression
1 eqbrtr.2 . 2 𝐵𝑅𝐶
2 eqbrtr.1 . . 3 𝐴 = 𝐵
32breq1i 4012 . 2 (𝐴𝑅𝐶𝐵𝑅𝐶)
41, 3mpbir 146 1 𝐴𝑅𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1353   class class class wbr 4005
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-un 3135  df-sn 3600  df-pr 3601  df-op 3603  df-br 4006
This theorem is referenced by:  eqbrtrri  4028  3brtr4i  4035  exmidonfinlem  7194  neg1lt0  9029  halflt1  9138  3halfnz  9352  declei  9421  numlti  9422  faclbnd3  10725  geo2lim  11526  0.999...  11531  geoihalfsum  11532  fprodap0  11631  fprodap0f  11646  tan0  11741  cos2bnd  11770  sin4lt0  11776  eirraplem  11786  1nprm  12116  znnen  12401  tan4thpi  14301  zabsle1  14439  ex-fl  14516  trilpolemisumle  14825
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