Metamath Proof Explorer

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 )