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 ( Cycles ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )

Proof

Step	Hyp	Ref	Expression
1		cyclispth	⊢ ( 𝐹 ( Cycles ‘ 𝐺 ) 𝑃 → 𝐹 ( Paths ‘ 𝐺 ) 𝑃 )
2		pthiswlk	⊢ ( 𝐹 ( Paths ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )
3	1 2	syl	⊢ ( 𝐹 ( Cycles ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )