Theorem eupthiswlk

Description: An Eulerian path is a walk. (Contributed by AV, 6-Apr-2021)

	Ref	Expression
Assertion	eupthiswlk	⊢ ( 𝐹 ( EulerPaths ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 )

Proof

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