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Theorem erclwwlknrel 25395
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 >.  |  ( t  e.  W  /\  u  e.  W  /\  E. n  e.  ( 0 ... N
) t  =  ( u cyclShift  n ) ) }
Assertion
Ref Expression
erclwwlknrel  |-  Rel  .~

Proof of Theorem erclwwlknrel
StepHypRef Expression
1 erclwwlkn.r . 2  |-  .~  =  { <. t ,  u >.  |  ( t  e.  W  /\  u  e.  W  /\  E. n  e.  ( 0 ... N
) t  =  ( u cyclShift  n ) ) }
21relopabi 4979 1  |-  Rel  .~
Colors of variables: wff setvar class
Syntax hints:    /\ w3a 982    = wceq 1437    e. wcel 1870   E.wrex 2783   {copab 4483   Rel wrel 4859   ` cfv 5601  (class class class)co 6305   0cc0 9538   ...cfz 11782   cyclShift ccsh 12875   ClWWalksN cclwwlkn 25322
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-opab 4485  df-xp 4860  df-rel 4861
This theorem is referenced by:  erclwwlkn  25401
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