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 ) C_ Word V

Proof

Step	Hyp	Ref	Expression
1		wwlkssswrd.v	|- V = ( Vtx ` G )
2	1	wwlkbp	|- ( w e. ( WWalks ` G ) -> ( G e. _V /\ w e. Word V ) )
3	2	simprd	|- ( w e. ( WWalks ` G ) -> w e. Word V )
4	3	ssriv	|- ( WWalks ` G ) C_ Word V