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Theorem erclwwlkneq 30646
 Description: Two classes are equivalent regarding if both are words of the same fixed length and one is the other cyclically shifted. (Contributed by Alexander van der Vekens, 25-Mar-2018.) (Revised by Alexander van der Vekens, 14-Jun-2018.)
Hypotheses
Ref Expression
erclwwlkn.w ClWWalksN
erclwwlkn.r cyclShift
Assertion
Ref Expression
erclwwlkneq cyclShift
Distinct variable groups:   ,,   ,,   ,,,   ,,   ,,,   ,,,
Allowed substitution hints:   (,,)   ()   ()   ()   (,,)   (,,)

Proof of Theorem erclwwlkneq
StepHypRef Expression
1 eleq1 2526 . . . 4
3 eleq1 2526 . . . 4
5 simpl 457 . . . . 5
6 oveq1 6208 . . . . . 6 cyclShift cyclShift
76adantl 466 . . . . 5 cyclShift cyclShift
85, 7eqeq12d 2476 . . . 4 cyclShift cyclShift
98rexbidv 2868 . . 3 cyclShift cyclShift
102, 4, 93anbi123d 1290 . 2 cyclShift cyclShift
11 erclwwlkn.r . 2 cyclShift
1210, 11brabga 4712 1 cyclShift
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 965   wceq 1370   wcel 1758  wrex 2800   class class class wbr 4401  copab 4458  cfv 5527  (class class class)co 6201  cc0 9394  cfz 11555   cyclShift ccsh 12544   ClWWalksN cclwwlkn 30563 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4522  ax-nul 4530  ax-pr 4640 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-br 4402  df-opab 4460  df-iota 5490  df-fv 5535  df-ov 6204 This theorem is referenced by:  erclwwlkneqlen  30647  erclwwlknref  30648  erclwwlknsym  30649  erclwwlkntr  30650  eclclwwlkn1  30655
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