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Theorem 3brtr4i 4480
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 4471 . 2  |-  C R B
4 3brtr4.3 . 2  |-  D  =  B
53, 4breqtrri 4477 1  |-  C R D
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379   class class class wbr 4452
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4453
This theorem is referenced by:  1lt2nq  9361  0lt1sr  9482  declt  11007  decltc  11008  fzennn  12056  faclbnd4lem1  12349  fsumabs  13590  ovolfiniun  21757  log2ublem3  23122  log2ub  23123  emgt0  23179  bclbnd  23398  bposlem8  23409  nmblolbii  25505  normlem6  25823  norm-ii-i  25845  nmbdoplbi  26734
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