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Theorem eqbrtrrd 3786
 Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999.)
Hypotheses
Ref Expression
eqbrtrrd.1 (𝜑𝐴 = 𝐵)
eqbrtrrd.2 (𝜑𝐴𝑅𝐶)
Assertion
Ref Expression
eqbrtrrd (𝜑𝐵𝑅𝐶)

Proof of Theorem eqbrtrrd
StepHypRef Expression
1 eqbrtrrd.1 . . 3 (𝜑𝐴 = 𝐵)
21eqcomd 2045 . 2 (𝜑𝐵 = 𝐴)
3 eqbrtrrd.2 . 2 (𝜑𝐴𝑅𝐶)
42, 3eqbrtrd 3784 1 (𝜑𝐵𝑅𝐶)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243   class class class wbr 3764 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765 This theorem is referenced by:  dftpos4  5878  phpm  6327  prmuloclemcalc  6663  mullocprlem  6668  cauappcvgprlemladdfl  6753  caucvgprlemopl  6767  caucvgprprlemloccalc  6782  caucvgprprlemopl  6795  ltadd1sr  6861  axarch  6965  lemulge11  7832  ltexp2a  9306  leexp2a  9307  nnlesq  9356  cvg1nlemcxze  9581  resqrexlemover  9608  resqrexlemlo  9611  resqrexlemnmsq  9615  resqrexlemnm  9616  leabs  9672  abs3dif  9701  abs2dif  9702  recn2  9837  imcn2  9838  iiserex  9859  nn0seqcvgd  9880
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