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Theorem eqbrtrrdi 3968
 Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
eqbrtrrdi.1 (𝜑𝐵 = 𝐴)
eqbrtrrdi.2 𝐵𝑅𝐶
Assertion
Ref Expression
eqbrtrrdi (𝜑𝐴𝑅𝐶)

Proof of Theorem eqbrtrrdi
StepHypRef Expression
1 eqbrtrrdi.1 . . 3 (𝜑𝐵 = 𝐴)
21eqcomd 2145 . 2 (𝜑𝐴 = 𝐵)
3 eqbrtrrdi.2 . 2 𝐵𝑅𝐶
42, 3eqbrtrdi 3967 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: (None)
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