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Theorem breqtri 4025
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 4008 . 2  |-  ( A R B  <->  A R C )
41, 3mpbi 145 1  |-  A R C
Colors of variables: wff set class
Syntax hints:    = wceq 1353   class class class wbr 4000
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-sn 3597  df-pr 3598  df-op 3600  df-br 4001
This theorem is referenced by:  breqtrri  4027  3brtr3i  4029  le9lt10  9399  9lt10  9503  sqrt2gt1lt2  11042  trireciplem  11492  cos1bnd  11751  cos2bnd  11752  cos01gt0  11754  sin4lt0  11758  z4even  11904  coseq00topi  13923  sincos4thpi  13928  lgsdir2lem2  14097  lgsdir2lem3  14098  ex-fl  14133
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