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Theorem 3brtr3i 4207
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 4201 . 2  |-  C R B
4 3brtr3.3 . 2  |-  B  =  D
53, 4breqtri 4203 1  |-  C R D
Colors of variables: wff set class
Syntax hints:    = wceq 1649   class class class wbr 4180
This theorem is referenced by:  supsrlem  8950  ef01bndlem  12748  pige3  20386  log2ublem1  20747  log2ub  20750  ppiublem1  20947  logfacrlim2  20971  chebbnd1  21127  nmoptri2i  23563
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-br 4181
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