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Theorem eqbrtrrdi 5072
 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 2764 . 2 (𝜑𝐴 = 𝐵)
3 eqbrtrrdi.2 . 2 𝐵𝑅𝐶
42, 3eqbrtrdi 5071 1 (𝜑𝐴𝑅𝐶)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1538   class class class wbr 5032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-v 3411  df-un 3863  df-sn 4523  df-pr 4525  df-op 4529  df-br 5033 This theorem is referenced by:  grur1  10280  t1connperf  22136  basellem9  25773  sqff1o  25866  ballotlemic  31992  ballotlem1c  31993  pibt2  35136
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