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Theorem erclwwlknrel 26350
Description: is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018.)
Hypotheses
Ref Expression
erclwwlkn.w 𝑊 = ((𝑉 ClWWalksN 𝐸)‘𝑁)
erclwwlkn.r = {⟨𝑡, 𝑢⟩ ∣ (𝑡𝑊𝑢𝑊 ∧ ∃𝑛 ∈ (0...𝑁)𝑡 = (𝑢 cyclShift 𝑛))}
Assertion
Ref Expression
erclwwlknrel Rel

Proof of Theorem erclwwlknrel
StepHypRef Expression
1 erclwwlkn.r . 2 = {⟨𝑡, 𝑢⟩ ∣ (𝑡𝑊𝑢𝑊 ∧ ∃𝑛 ∈ (0...𝑁)𝑡 = (𝑢 cyclShift 𝑛))}
21relopabi 5167 1 Rel
Colors of variables: wff setvar class
Syntax hints:  w3a 1031   = wceq 1475  wcel 1977  wrex 2897  {copab 4642  Rel wrel 5043  cfv 5804  (class class class)co 6549  0cc0 9815  ...cfz 12197   cyclShift ccsh 13385   ClWWalksN cclwwlkn 26277
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-opab 4644  df-xp 5044  df-rel 5045
This theorem is referenced by:  erclwwlkn  26356
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