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Theorem 3brtr3d 3783
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 18-Oct-1999.)
Hypotheses
Ref Expression
3brtr3d.1  R
3brtr3d.2  C
3brtr3d.3  D
Assertion
Ref Expression
3brtr3d  C R D

Proof of Theorem 3brtr3d
StepHypRef Expression
1 3brtr3d.1 . 2  R
2 3brtr3d.2 . . 3  C
3 3brtr3d.3 . . 3  D
42, 3breq12d 3767 . 2  R  C R D
51, 4mpbid 135 1  C R D
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   class class class wbr 3754
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 3372  df-pr 3373  df-op 3375  df-br 3755
This theorem is referenced by:  ofrval  5661  ltaddnq  6383  prarloclemarch2  6395  prmuloclemcalc  6536  apreap  7323  ltmul1  7328  divap1d  7510  lemul2a  7557
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