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Theorem 3brtr4i 4613
 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 4604 . 2 𝐶𝑅𝐵
4 3brtr4.3 . 2 𝐷 = 𝐵
53, 4breqtrri 4610 1 𝐶𝑅𝐷
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   class class class wbr 4583 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-br 4584 This theorem is referenced by:  1lt2nq  9674  0lt1sr  9795  declt  11406  decltOLD  11407  decltc  11408  decltcOLD  11409  decle  11416  decleOLD  11419  fzennn  12629  faclbnd4lem1  12942  fsumabs  14374  ovolfiniun  23076  log2ublem3  24475  log2ub  24476  emgt0  24533  bclbnd  24805  bposlem8  24816  baseltedgf  25671  nmblolbii  27038  normlem6  27356  norm-ii-i  27378  nmbdoplbi  28267  nnsum4primesevenALTV  40217
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