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Theorem eqbrtrrid 3964
Description: B chained equality inference for a binary relation. (Contributed by NM, 17-Sep-2004.)
Hypotheses
Ref Expression
eqbrtrrid.1 𝐵 = 𝐴
eqbrtrrid.2 (𝜑𝐵𝑅𝐶)
Assertion
Ref Expression
eqbrtrrid (𝜑𝐴𝑅𝐶)

Proof of Theorem eqbrtrrid
StepHypRef Expression
1 eqbrtrrid.2 . 2 (𝜑𝐵𝑅𝐶)
2 eqbrtrrid.1 . 2 𝐵 = 𝐴
3 eqid 2139 . 2 𝐶 = 𝐶
41, 2, 33brtr3g 3961 1 (𝜑𝐴𝑅𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1331   class class class wbr 3929
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930
This theorem is referenced by:  enpr1g  6692  endjudisj  7066  recexprlem1ssl  7448  addgt0  8217  addgegt0  8218  addgtge0  8219  addge0  8220  expge1  10337  expcnv  11280  cos12dec  11481  ncoprmgcdne1b  11777  phicl2  11897  exmidunben  11946  sin0pilem2  12876  cosq23lt0  12927  cos0pilt1  12946
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