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Metamath Proof Explorer

Theorem pthiswlk

Description: A path is a walk (in an undirected graph). (Contributed by AV, 6-Feb-2021)

Ref Expression
Assertion pthiswlk 
|- ( F ( Paths ` G ) P -> F ( Walks ` G ) P )

Proof

Step Hyp Ref Expression
1 pthistrl 
 |-  ( F ( Paths ` G ) P -> F ( Trails ` G ) P )
2 trliswlk 
 |-  ( F ( Trails ` G ) P -> F ( Walks ` G ) P )
3 1 2 syl 
 |-  ( F ( Paths ` G ) P -> F ( Walks ` G ) P )