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Theorem erclwwlkrel 29270
Description: ∼ is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018.) (Revised by AV, 29-Apr-2021.)
Hypothesis
Ref Expression
erclwwlk.r ∼ = {βŸ¨π‘’, π‘€βŸ© ∣ (𝑒 ∈ (ClWWalksβ€˜πΊ) ∧ 𝑀 ∈ (ClWWalksβ€˜πΊ) ∧ βˆƒπ‘› ∈ (0...(β™―β€˜π‘€))𝑒 = (𝑀 cyclShift 𝑛))}
Assertion
Ref Expression
erclwwlkrel Rel ∼

Proof of Theorem erclwwlkrel
StepHypRef Expression
1 erclwwlk.r . 2 ∼ = {βŸ¨π‘’, π‘€βŸ© ∣ (𝑒 ∈ (ClWWalksβ€˜πΊ) ∧ 𝑀 ∈ (ClWWalksβ€˜πΊ) ∧ βˆƒπ‘› ∈ (0...(β™―β€˜π‘€))𝑒 = (𝑀 cyclShift 𝑛))}
21relopabi 5823 1 Rel ∼
Colors of variables: wff setvar class
Syntax hints:   ∧ w3a 1088   = wceq 1542   ∈ wcel 2107  βˆƒwrex 3071  {copab 5211  Rel wrel 5682  β€˜cfv 6544  (class class class)co 7409  0cc0 11110  ...cfz 13484  β™―chash 14290   cyclShift ccsh 14738  ClWWalkscclwwlk 29234
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-11 2155  ax-12 2172  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-opab 5212  df-xp 5683  df-rel 5684
This theorem is referenced by:  erclwwlk  29276
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