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Theorem 3brtr3i 4231
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 4225 . 2  |-  C R B
4 3brtr3.3 . 2  |-  B  =  D
53, 4breqtri 4227 1  |-  C R D
Colors of variables: wff set class
Syntax hints:    = wceq 1652   class class class wbr 4204
This theorem is referenced by:  supsrlem  8976  ef01bndlem  12775  pige3  20415  log2ublem1  20776  log2ub  20779  ppiublem1  20976  logfacrlim2  21000  chebbnd1  21156  nmoptri2i  23592
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205
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