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Theorem 3brtr4i 4645
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 4636 . 2 𝐶𝑅𝐵
4 3brtr4.3 . 2 𝐷 = 𝐵
53, 4breqtrri 4642 1 𝐶𝑅𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480   class class class wbr 4615
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rab 2916  df-v 3188  df-dif 3559  df-un 3561  df-in 3563  df-ss 3570  df-nul 3894  df-if 4061  df-sn 4151  df-pr 4153  df-op 4157  df-br 4616
This theorem is referenced by:  1lt2nq  9742  0lt1sr  9863  declt  11477  decltOLD  11478  decltc  11479  decltcOLD  11480  decle  11487  decleOLD  11490  fzennn  12710  faclbnd4lem1  13023  fsumabs  14463  ovolfiniun  23182  log2ublem3  24582  log2ub  24583  emgt0  24640  bclbnd  24912  bposlem8  24923  baseltedgf  25779  nmblolbii  27515  normlem6  27833  norm-ii-i  27855  nmbdoplbi  28744  nnsum4primesevenALTV  40994
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