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Theorem syl6eqbr 3792
Description: A chained equality inference for a binary relation. (Contributed by NM, 12-Oct-1999.)
Hypotheses
Ref Expression
syl6eqbr.1
syl6eqbr.2  R C
Assertion
Ref Expression
syl6eqbr  R C

Proof of Theorem syl6eqbr
StepHypRef Expression
1 syl6eqbr.2 . 2  R C
2 syl6eqbr.1 . . 3
32breq1d 3765 . 2  R C  R C
41, 3mpbiri 157 1  R C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   class class class wbr 3755
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756
This theorem is referenced by:  syl6eqbrr  3793  xltnegi  8518  leexp1a  8963
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