Theorem erclwwlksnrel 26943

Description: .~ is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018.) (Revised by AV, 30-Apr-2021.)

Hypotheses

Ref	Expression
erclwwlksn.w	|- W = ( N ClWWalksN G )
erclwwlksn.r	|- .~ = { <. t , u >. | ( t e. W /\ u e. W /\ E. n e. ( 0 ... N ) t = ( u cyclShift n ) ) }

Assertion

Ref	Expression
erclwwlksnrel	|- Rel .~

Proof of Theorem erclwwlksnrel

Step	Hyp	Ref	Expression
1		erclwwlksn.r	. 2 |- .~ = { <. t , u >. | ( t e. W /\ u e. W /\ E. n e. ( 0 ... N ) t = ( u cyclShift n ) ) }
2	1	relopabi 5245	1 |- Rel .~

Syntax hints:   /\ w3a 1037   = wceq 1483   e. wcel 1990   E.wrex 2913   {copab 4712   Rel wrel 5119  (class class class)co 6650   0cc0 9936   ...cfz 12326   cyclShift ccsh 13534   ClWWalksN cclwwlksn 26876

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-nul 3916  df-if 4087  df-sn 4178  df-pr 4180  df-op 4184  df-opab 4713  df-xp 5120  df-rel 5121

This theorem is referenced by:  erclwwlksn  26949