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Theorem eqbrtrid 3963
Description: B chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999.)
Hypotheses
Ref Expression
eqbrtrid.1  |-  A  =  B
eqbrtrid.2  |-  ( ph  ->  B R C )
Assertion
Ref Expression
eqbrtrid  |-  ( ph  ->  A R C )

Proof of Theorem eqbrtrid
StepHypRef Expression
1 eqbrtrid.2 . 2  |-  ( ph  ->  B R C )
2 eqbrtrid.1 . 2  |-  A  =  B
3 eqid 2139 . 2  |-  C  =  C
41, 2, 33brtr4g 3962 1  |-  ( ph  ->  A R C )
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:  xp1en  6717  caucvgprlemm  7483  intqfrac2  10099  m1modge3gt1  10151  bernneq2  10420  reccn2ap  11089  eirraplem  11489  nno  11609  oddprmge3  11821  sqnprm  11822  oddennn  11911  strle2g  12059  strle3g  12060  1strstrg  12066  2strstrg  12068  rngstrg  12083  srngstrd  12090  lmodstrd  12101  ipsstrd  12109  topgrpstrd  12119  psmetge0  12509  reeff1olem  12869  cosq14gt0  12929  cosq34lt1  12947  ioocosf1o  12951  pwf1oexmid  13247  trilpolemeq1  13286
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