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Theorem 3brtr3i 5096
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr3.1 𝐴𝑅𝐵
3brtr3.2 𝐴 = 𝐶
3brtr3.3 𝐵 = 𝐷
Assertion
Ref Expression
3brtr3i 𝐶𝑅𝐷

Proof of Theorem 3brtr3i
StepHypRef Expression
1 3brtr3.2 . . 3 𝐴 = 𝐶
2 3brtr3.1 . . 3 𝐴𝑅𝐵
31, 2eqbrtrri 5090 . 2 𝐶𝑅𝐵
4 3brtr3.3 . 2 𝐵 = 𝐷
53, 4breqtri 5092 1 𝐶𝑅𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1543   class class class wbr 5067
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-ext 2709
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-3an 1091  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3071  df-v 3422  df-dif 3883  df-un 3885  df-nul 4252  df-if 4454  df-sn 4556  df-pr 4558  df-op 4562  df-br 5068
This theorem is referenced by:  supsrlem  10749  ef01bndlem  15769  pige3ALT  25433  log2ublem1  25853  log2ub  25856  ppiublem1  26107  logfacrlim2  26131  chebbnd1  26377  nmoptri2i  30204  dpmul4  30932  problem5  33363  fouriersw  43475
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