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Theorem eqbrtri 3774
Description: Substitution of equal classes into a binary relation. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
eqbrtr.1 A = B
eqbrtr.2 B𝑅𝐶
Assertion
Ref Expression
eqbrtri A𝑅𝐶

Proof of Theorem eqbrtri
StepHypRef Expression
1 eqbrtr.2 . 2 B𝑅𝐶
2 eqbrtr.1 . . 3 A = B
32breq1i 3762 . 2 (A𝑅𝐶B𝑅𝐶)
41, 3mpbir 134 1 A𝑅𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1242   class class class wbr 3755
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756
This theorem is referenced by:  eqbrtrri  3776  3brtr4i  3783  neg1lt0  7763  halflt1  7879  numlti  8127
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