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Theorem eqbrtrri 4023
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 2181 . 2  |-  B  =  A
3 eqbrtrr.2 . 2  |-  A R C
42, 3eqbrtri 4021 1  |-  B 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:  3brtr3i  4029  dju1p1e2  7189  expnass  10598  sqrt2gt1lt2  11029  cos1bnd  11738  cos2bnd  11739  infpn2  12427  2strstr1g  12546  coseq00topi  13889  pigt3  13898
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