Metamath Proof Explorer


Theorem trliswlk

Description: A trail is a walk. (Contributed by Alexander van der Vekens, 20-Oct-2017) (Revised by AV, 7-Jan-2021) (Proof shortened by AV, 29-Oct-2021)

Ref Expression
Assertion trliswlk
|- ( F ( Trails ` G ) P -> F ( Walks ` G ) P )

Proof

Step Hyp Ref Expression
1 istrl
 |-  ( F ( Trails ` G ) P <-> ( F ( Walks ` G ) P /\ Fun `' F ) )
2 1 simplbi
 |-  ( F ( Trails ` G ) P -> F ( Walks ` G ) P )