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Theorem syl6eqbrr 4250
Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl6eqbrr.1  |-  ( ph  ->  B  =  A )
syl6eqbrr.2  |-  B R C
Assertion
Ref Expression
syl6eqbrr  |-  ( ph  ->  A R C )

Proof of Theorem syl6eqbrr
StepHypRef Expression
1 syl6eqbrr.1 . . 3  |-  ( ph  ->  B  =  A )
21eqcomd 2441 . 2  |-  ( ph  ->  A  =  B )
3 syl6eqbrr.2 . 2  |-  B R C
42, 3syl6eqbr 4249 1  |-  ( ph  ->  A R C )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   class class class wbr 4212
This theorem is referenced by:  grur1  8695  t1conperf  17499  basellem9  20871  sqff1o  20965  ballotlemic  24764  ballotlem1c  24765
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213
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