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Theorem 3brtr3i 4464
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr3.1  |-  A R B
3brtr3.2  |-  A  =  C
3brtr3.3  |-  B  =  D
Assertion
Ref Expression
3brtr3i  |-  C R D

Proof of Theorem 3brtr3i
StepHypRef Expression
1 3brtr3.2 . . 3  |-  A  =  C
2 3brtr3.1 . . 3  |-  A R B
31, 2eqbrtrri 4458 . 2  |-  C R B
4 3brtr3.3 . 2  |-  B  =  D
53, 4breqtri 4460 1  |-  C R D
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383   class class class wbr 4437
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-br 4438
This theorem is referenced by:  supsrlem  9491  ef01bndlem  13901  pige3  22888  log2ublem1  23255  log2ub  23258  ppiublem1  23455  logfacrlim2  23479  chebbnd1  23635  nmoptri2i  26996  problem5  29001  fouriersw  31968
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