Metamath Proof Explorer

Theorem eupthistrl

Description: An Eulerian path is a trail. (Contributed by Alexander van der Vekens, 24-Nov-2017) (Revised by AV, 18-Feb-2021)

Ref Expression
Assertion eupthistrl 
|- ( F ( EulerPaths ` G ) P -> F ( Trails ` G ) P )

Proof

Step Hyp Ref Expression
1 eqid 
 |-  ( iEdg ` G ) = ( iEdg ` G )
2 1 iseupth 
 |-  ( F ( EulerPaths ` G ) P <-> ( F ( Trails ` G ) P /\ F : ( 0 ..^ ( # ` F ) ) -onto-> dom ( iEdg ` G ) ) )
3 2 simplbi 
 |-  ( F ( EulerPaths ` G ) P -> F ( Trails ` G ) P )