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	$$⊢V=\mathrm{Vtx}\left(G\right)$$
Assertion	wwlkssswrd	$$⊢\mathrm{WWalks}\left(G\right)\subseteq \mathrm{Word}V$$

Proof

Step	Hyp	Ref	Expression
1		wwlkssswrd.v	$$⊢V=\mathrm{Vtx}\left(G\right)$$
2	1	wwlkbp	$$⊢w\in \mathrm{WWalks}\left(G\right)\to \left(G\in \mathrm{V}\wedge w\in \mathrm{Word}V\right)$$
3	2	simprd	$$⊢w\in \mathrm{WWalks}\left(G\right)\to w\in \mathrm{Word}V$$
4	3	ssriv	$$⊢\mathrm{WWalks}\left(G\right)\subseteq \mathrm{Word}V$$