Theorem wwlkssswrd

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