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Theorem eqbrtrri 3951
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtrr.1 𝐴 = 𝐵
eqbrtrr.2 𝐴𝑅𝐶
Assertion
Ref Expression
eqbrtrri 𝐵𝑅𝐶

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3 𝐴 = 𝐵
21eqcomi 2143 . 2 𝐵 = 𝐴
3 eqbrtrr.2 . 2 𝐴𝑅𝐶
42, 3eqbrtri 3949 1 𝐵𝑅𝐶
Colors of variables: wff set class
Syntax hints:   = 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:  3brtr3i  3957  dju1p1e2  7058  expnass  10410  sqrt2gt1lt2  10833  cos1bnd  11477  cos2bnd  11478  2strstr1g  12076  coseq00topi  12938  pigt3  12947
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