This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Walks (represented by words) are words. (Contributed by Alexander van
der Vekens, 17-Jul-2018) (Revised by AV, 9-Apr-2021)
|
|
Ref |
Expression |
|
Hypothesis |
wwlkssswrd.v |
⊢ 𝑉 = ( Vtx ‘ 𝐺 ) |
|
Assertion |
wwlkssswrd |
⊢ ( WWalks ‘ 𝐺 ) ⊆ Word 𝑉 |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
wwlkssswrd.v |
⊢ 𝑉 = ( Vtx ‘ 𝐺 ) |
| 2 |
1
|
wwlkbp |
⊢ ( 𝑤 ∈ ( WWalks ‘ 𝐺 ) → ( 𝐺 ∈ V ∧ 𝑤 ∈ Word 𝑉 ) ) |
| 3 |
2
|
simprd |
⊢ ( 𝑤 ∈ ( WWalks ‘ 𝐺 ) → 𝑤 ∈ Word 𝑉 ) |
| 4 |
3
|
ssriv |
⊢ ( WWalks ‘ 𝐺 ) ⊆ Word 𝑉 |