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Theorem 3brtr4i 4067
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 4058 . 2  |-  C R B
4 3brtr4.3 . 2  |-  D  =  B
53, 4breqtrri 4064 1  |-  C R D
Colors of variables: wff set class
Syntax hints:    = wceq 1632   class class class wbr 4039
This theorem is referenced by:  1lt2nq  8613  0lt1sr  8733  declt  10161  decltc  10162  fzennn  11046  faclbnd4lem1  11322  fsumabs  12275  ovolfiniun  18876  log2ublem3  20260  log2ub  20261  emgt0  20316  bclbnd  20535  bposlem8  20546  nmblolbii  21393  normlem6  21710  norm-ii-i  21732  nmbdoplbi  22620
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040
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