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Theorem breqtrrdi 3970
Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005.)
Hypotheses
Ref Expression
breqtrrdi.1  |-  ( ph  ->  A R B )
breqtrrdi.2  |-  C  =  B
Assertion
Ref Expression
breqtrrdi  |-  ( ph  ->  A R C )

Proof of Theorem breqtrrdi
StepHypRef Expression
1 breqtrrdi.1 . 2  |-  ( ph  ->  A R B )
2 breqtrrdi.2 . . 3  |-  C  =  B
32eqcomi 2143 . 2  |-  B  =  C
41, 3breqtrdi 3969 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:  enpr2d  6711  fiunsnnn  6775  unsnfi  6807  eninl  6982  eninr  6983  difinfinf  6986  exmidfodomrlemr  7058  exmidfodomrlemrALT  7059  dju1en  7069  djucomen  7072  djuassen  7073  xpdjuen  7074  gtndiv  9153  intqfrac2  10099  uzenom  10205  xrmaxiflemval  11026  ege2le3  11384  eirraplem  11490  2strstr1g  12072  lmcn2  12459  dveflem  12865  tangtx  12932  ioocosf1o  12948  sbthom  13251
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