Theorem crctistrl

Description: A circuit is a trail. (Contributed by Alexander van der Vekens, 30-Oct-2017) (Revised by AV, 31-Jan-2021)

	Ref	Expression
Assertion	crctistrl	⊢ ( 𝐹 ( Circuits ‘ 𝐺 ) 𝑃 → 𝐹 ( Trails ‘ 𝐺 ) 𝑃 )

Proof

Step	Hyp	Ref	Expression
1		crctprop	⊢ ( 𝐹 ( Circuits ‘ 𝐺 ) 𝑃 → ( 𝐹 ( Trails ‘ 𝐺 ) 𝑃 ∧ ( 𝑃 ‘ 0 ) = ( 𝑃 ‘ ( ♯ ‘ 𝐹 ) ) ) )
2	1	simpld	⊢ ( 𝐹 ( Circuits ‘ 𝐺 ) 𝑃 → 𝐹 ( Trails ‘ 𝐺 ) 𝑃 )