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Theorem 3brtr4i 5072
Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 11-Aug-1999.)
Hypotheses
Ref Expression
3brtr4.1 𝐴𝑅𝐵
3brtr4.2 𝐶 = 𝐴
3brtr4.3 𝐷 = 𝐵
Assertion
Ref Expression
3brtr4i 𝐶𝑅𝐷

Proof of Theorem 3brtr4i
StepHypRef Expression
1 3brtr4.2 . . 3 𝐶 = 𝐴
2 3brtr4.1 . . 3 𝐴𝑅𝐵
31, 2eqbrtri 5063 . 2 𝐶𝑅𝐵
4 3brtr4.3 . 2 𝐷 = 𝐵
53, 4breqtrri 5069 1 𝐶𝑅𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538   class class class wbr 5042
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-un 3913  df-sn 4540  df-pr 4542  df-op 4546  df-br 5043
This theorem is referenced by:  1lt2nq  10384  0lt1sr  10506  declt  12114  decltc  12115  decle  12120  fzennn  13331  faclbnd4lem1  13649  fsumabs  15147  ovolfiniun  24103  log2ublem3  25532  log2ub  25533  bclbnd  25862  bposlem8  25873  baseltedgf  26785  nmblolbii  28580  normlem6  28896  norm-ii-i  28918  nmbdoplbi  29805  dp2lt  30571  dp2ltsuc  30572  dp2ltc  30573  dplt  30590  dpltc  30593  dpmul4  30600  hgt750lemd  31993  hgt750lem  31996  3lexlogpow5ineq2  39304  supxrltinfxr  42027  nnsum4primesevenALTV  44259
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