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Theorem syl6eqbrr 4623
 Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl6eqbrr.1 (𝜑𝐵 = 𝐴)
syl6eqbrr.2 𝐵𝑅𝐶
Assertion
Ref Expression
syl6eqbrr (𝜑𝐴𝑅𝐶)

Proof of Theorem syl6eqbrr
StepHypRef Expression
1 syl6eqbrr.1 . . 3 (𝜑𝐵 = 𝐴)
21eqcomd 2616 . 2 (𝜑𝐴 = 𝐵)
3 syl6eqbrr.2 . 2 𝐵𝑅𝐶
42, 3syl6eqbr 4622 1 (𝜑𝐴𝑅𝐶)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   class class class wbr 4583 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584 This theorem is referenced by:  grur1  9521  t1conperf  21049  basellem9  24615  sqff1o  24708  ballotlemic  29895  ballotlem1c  29896
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