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Theorem 3brtr4i 4431
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 4422 . 2  |-  C R B
4 3brtr4.3 . 2  |-  D  =  B
53, 4breqtrri 4428 1  |-  C R D
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   class class class wbr 4403
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-br 4404
This theorem is referenced by:  1lt2nq  9257  0lt1sr  9377  declt  10891  decltc  10892  fzennn  11911  faclbnd4lem1  12190  fsumabs  13386  ovolfiniun  21126  log2ublem3  22486  log2ub  22487  emgt0  22543  bclbnd  22762  bposlem8  22773  nmblolbii  24378  normlem6  24696  norm-ii-i  24718  nmbdoplbi  25607
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