Metamath Proof Explorer

Theorem cyclispth

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

Ref Expression
Assertion cyclispth 
|- ( F ( Cycles ` G ) P -> F ( Paths ` G ) P )

Proof

Step Hyp Ref Expression
1 cyclprop 
 |-  ( F ( Cycles ` G ) P -> ( F ( Paths ` G ) P /\ ( P ` 0 ) = ( P ` ( # ` F ) ) ) )
2 1 simpld 
 |-  ( F ( Cycles ` G ) P -> F ( Paths ` G ) P )