Theorem wlkpwrd

Description: The sequence of vertices of a walk is a word over the set of vertices. (Contributed by AV, 27-Jan-2021)

	Ref	Expression
Hypothesis	wlkp.v	⊢ 𝑉 = ( Vtx ‘ 𝐺 )
Assertion	wlkpwrd	⊢ ( 𝐹 ( Walks ‘ 𝐺 ) 𝑃 → 𝑃 ∈ Word 𝑉 )

Proof

Step	Hyp	Ref	Expression
1		wlkp.v	⊢ 𝑉 = ( Vtx ‘ 𝐺 )
2	1	wlkp	⊢ ( 𝐹 ( Walks ‘ 𝐺 ) 𝑃 → 𝑃 : ( 0 ... ( ♯ ‘ 𝐹 ) ) ⟶ 𝑉 )
3		ffz0iswrd	⊢ ( 𝑃 : ( 0 ... ( ♯ ‘ 𝐹 ) ) ⟶ 𝑉 → 𝑃 ∈ Word 𝑉 )
4	2 3	syl	⊢ ( 𝐹 ( Walks ‘ 𝐺 ) 𝑃 → 𝑃 ∈ Word 𝑉 )