Metamath Proof Explorer

Theorem clwwlknlen

Description: The length of a word representing a closed walk of a fixed length is this fixed length. (Contributed by AV, 22-Mar-2022)

Ref Expression
Assertion clwwlknlen 
|- ( W e. ( N ClWWalksN G ) -> ( # ` W ) = N )

Proof

Step Hyp Ref Expression
1 isclwwlkn 
 |-  ( W e. ( N ClWWalksN G ) <-> ( W e. ( ClWWalks ` G ) /\ ( # ` W ) = N ) )
2 1 simprbi 
 |-  ( W e. ( N ClWWalksN G ) -> ( # ` W ) = N )