Theorem clwlkswks

Description: Closed walks are walks (in an undirected graph). (Contributed by Alexander van der Vekens, 25-Aug-2018) (Revised by AV, 16-Feb-2021)

	Ref	Expression
Assertion	clwlkswks	⊢ ( ClWalks ‘ 𝐺 ) ⊆ ( Walks ‘ 𝐺 )

Proof

Step	Hyp	Ref	Expression
1		clwlkwlk	⊢ ( 𝑤 ∈ ( ClWalks ‘ 𝐺 ) → 𝑤 ∈ ( Walks ‘ 𝐺 ) )
2	1	ssriv	⊢ ( ClWalks ‘ 𝐺 ) ⊆ ( Walks ‘ 𝐺 )