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Theorem eqbrtrri 3921
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtrr.1  |-  A  =  B
eqbrtrr.2  |-  A R C
Assertion
Ref Expression
eqbrtrri  |-  B R C

Proof of Theorem eqbrtrri
StepHypRef Expression
1 eqbrtrr.1 . . 3  |-  A  =  B
21eqcomi 2121 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 3919 1  |-  B R C
Colors of variables: wff set class
Syntax hints:    = wceq 1316   class class class wbr 3899
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900
This theorem is referenced by:  3brtr3i  3927  dju1p1e2  7021  expnass  10366  sqrt2gt1lt2  10789  cos1bnd  11393  cos2bnd  11394  2strstr1g  11989  coseq00topi  12843  pigt3  12852
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