Theorem pthiswlk

Description: A path is a walk (in an undirected graph). (Contributed by AV, 6-Feb-2021)

	Ref	Expression
Assertion	pthiswlk	⊢ ( 𝐹 ( Paths ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )

Proof

Step	Hyp	Ref	Expression
1		pthistrl	⊢ ( 𝐹 ( Paths ‘ 𝐺 ) 𝑃 → 𝐹 ( Trails ‘ 𝐺 ) 𝑃 )
2		trliswlk	⊢ ( 𝐹 ( Trails ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )
3	1 2	syl	⊢ ( 𝐹 ( Paths ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )