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Theorem 3brtr3i 5177
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 5171 . 2 𝐶𝑅𝐵
4 3brtr3.3 . 2 𝐵 = 𝐷
53, 4breqtri 5173 1 𝐶𝑅𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537   class class class wbr 5148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-br 5149
This theorem is referenced by:  supsrlem  11149  ef01bndlem  16217  pige3ALT  26577  log2ublem1  27004  log2ub  27007  ppiublem1  27261  logfacrlim2  27285  chebbnd1  27531  nmoptri2i  32128  dpmul4  32881  problem5  35654  fouriersw  46187
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