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Theorem breqtri 3956
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
breqtr.1  |-  A R B
breqtr.2  |-  B  =  C
Assertion
Ref Expression
breqtri  |-  A R C

Proof of Theorem breqtri
StepHypRef Expression
1 breqtr.1 . 2  |-  A R B
2 breqtr.2 . . 3  |-  B  =  C
32breq2i 3940 . 2  |-  ( A R B  <->  A R C )
41, 3mpbi 144 1  |-  A R C
Colors of variables: wff set class
Syntax hints:    = wceq 1331   class class class wbr 3932
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 3933
This theorem is referenced by:  breqtrri  3958  3brtr3i  3960  le9lt10  9227  9lt10  9331  sqrt2gt1lt2  10845  trireciplem  11293  cos1bnd  11489  cos2bnd  11490  cos01gt0  11492  sin4lt0  11496  z4even  11636  coseq00topi  12950  sincos4thpi  12955  ex-fl  13081
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