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Mirrors > Home > MPE Home > Th. List > erclwwlkrel | Structured version Visualization version GIF version |
Description: βΌ is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018.) (Revised by AV, 29-Apr-2021.) |
Ref | Expression |
---|---|
erclwwlk.r | β’ βΌ = {β¨π’, π€β© β£ (π’ β (ClWWalksβπΊ) β§ π€ β (ClWWalksβπΊ) β§ βπ β (0...(β―βπ€))π’ = (π€ cyclShift π))} |
Ref | Expression |
---|---|
erclwwlkrel | β’ Rel βΌ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | erclwwlk.r | . 2 β’ βΌ = {β¨π’, π€β© β£ (π’ β (ClWWalksβπΊ) β§ π€ β (ClWWalksβπΊ) β§ βπ β (0...(β―βπ€))π’ = (π€ cyclShift π))} | |
2 | 1 | relopabi 5782 | 1 β’ Rel βΌ |
Colors of variables: wff setvar class |
Syntax hints: β§ w3a 1088 = wceq 1542 β wcel 2107 βwrex 3070 {copab 5171 Rel wrel 5642 βcfv 6500 (class class class)co 7361 0cc0 11059 ...cfz 13433 β―chash 14239 cyclShift ccsh 14685 ClWWalkscclwwlk 28974 |
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 3407 df-v 3449 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-opab 5172 df-xp 5643 df-rel 5644 |
This theorem is referenced by: erclwwlk 29016 |
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