Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > erclwwlknrel | Structured version Visualization version GIF version |
Description: ∼ is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018.) (Revised by AV, 30-Apr-2021.) |
Ref | Expression |
---|---|
erclwwlkn.w | ⊢ 𝑊 = (𝑁 ClWWalksN 𝐺) |
erclwwlkn.r | ⊢ ∼ = {〈𝑡, 𝑢〉 ∣ (𝑡 ∈ 𝑊 ∧ 𝑢 ∈ 𝑊 ∧ ∃𝑛 ∈ (0...𝑁)𝑡 = (𝑢 cyclShift 𝑛))} |
Ref | Expression |
---|---|
erclwwlknrel | ⊢ Rel ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | erclwwlkn.r | . 2 ⊢ ∼ = {〈𝑡, 𝑢〉 ∣ (𝑡 ∈ 𝑊 ∧ 𝑢 ∈ 𝑊 ∧ ∃𝑛 ∈ (0...𝑁)𝑡 = (𝑢 cyclShift 𝑛))} | |
2 | 1 | relopabi 5692 | 1 ⊢ Rel ∼ |
Colors of variables: wff setvar class |
Syntax hints: ∧ w3a 1089 = wceq 1543 ∈ wcel 2110 ∃wrex 3062 {copab 5115 Rel wrel 5556 (class class class)co 7213 0cc0 10729 ...cfz 13095 cyclShift ccsh 14353 ClWWalksN cclwwlkn 28107 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-11 2158 ax-12 2175 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3an 1091 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3070 df-v 3410 df-dif 3869 df-un 3871 df-in 3873 df-ss 3883 df-nul 4238 df-if 4440 df-sn 4542 df-pr 4544 df-op 4548 df-opab 5116 df-xp 5557 df-rel 5558 |
This theorem is referenced by: erclwwlkn 28155 |
Copyright terms: Public domain | W3C validator |