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Theorem 3brtr4i 4240
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr4.1  |-  A R B
3brtr4.2  |-  C  =  A
3brtr4.3  |-  D  =  B
Assertion
Ref Expression
3brtr4i  |-  C R D

Proof of Theorem 3brtr4i
StepHypRef Expression
1 3brtr4.2 . . 3  |-  C  =  A
2 3brtr4.1 . . 3  |-  A R B
31, 2eqbrtri 4231 . 2  |-  C R B
4 3brtr4.3 . 2  |-  D  =  B
53, 4breqtrri 4237 1  |-  C R D
Colors of variables: wff set class
Syntax hints:    = wceq 1652   class class class wbr 4212
This theorem is referenced by:  1lt2nq  8850  0lt1sr  8970  declt  10403  decltc  10404  fzennn  11307  faclbnd4lem1  11584  fsumabs  12580  ovolfiniun  19397  log2ublem3  20788  log2ub  20789  emgt0  20845  bclbnd  21064  bposlem8  21075  nmblolbii  22300  normlem6  22617  norm-ii-i  22639  nmbdoplbi  23527
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 2417
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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213
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