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Theorem 3brtr4i 4308
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 4299 . 2  |-  C R B
4 3brtr4.3 . 2  |-  D  =  B
53, 4breqtrri 4305 1  |-  C R D
Colors of variables: wff setvar class
Syntax hints:    = wceq 1362   class class class wbr 4280
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1594  ax-4 1605  ax-5 1669  ax-6 1707  ax-7 1727  ax-10 1774  ax-11 1779  ax-12 1791  ax-13 1942  ax-ext 2414
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 960  df-tru 1365  df-ex 1590  df-nf 1593  df-sb 1700  df-clab 2420  df-cleq 2426  df-clel 2429  df-nfc 2558  df-rab 2714  df-v 2964  df-dif 3319  df-un 3321  df-in 3323  df-ss 3330  df-nul 3626  df-if 3780  df-sn 3866  df-pr 3868  df-op 3872  df-br 4281
This theorem is referenced by:  1lt2nq  9130  0lt1sr  9250  declt  10764  decltc  10765  fzennn  11774  faclbnd4lem1  12053  fsumabs  13247  ovolfiniun  20826  log2ublem3  22228  log2ub  22229  emgt0  22285  bclbnd  22504  bposlem8  22515  nmblolbii  24022  normlem6  24340  norm-ii-i  24362  nmbdoplbi  25251
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