Theorem cycliswlk

Description: A cycle is a walk. (Contributed by Alexander van der Vekens, 7-Nov-2017) (Revised by AV, 31-Jan-2021)

	Ref	Expression
Assertion	cycliswlk	$$⊢F\mathrm{Cycles}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$

Proof

Step	Hyp	Ref	Expression
1		cyclispth	$$⊢F\mathrm{Cycles}\left(G\right)P\to F\mathrm{Paths}\left(G\right)P$$
2		pthiswlk	$$⊢F\mathrm{Paths}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$
3	1 2	syl	$$⊢F\mathrm{Cycles}\left(G\right)P\to F\mathrm{Walks}\left(G\right)P$$