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Theorem eqbrtrri 4041
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 2193 . 2 𝐵 = 𝐴
3 eqbrtrr.2 . 2 𝐴𝑅𝐶
42, 3eqbrtri 4039 1 𝐵𝑅𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1364   class class class wbr 4018
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-op 3616  df-br 4019
This theorem is referenced by:  3brtr3i  4047  dju1p1e2  7225  expnass  10656  sqrt2gt1lt2  11089  cos1bnd  11798  cos2bnd  11799  infpn2  12506  2strstr1g  12630  coseq00topi  14708  pigt3  14717
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