Metamath Proof Explorer

Theorem s4fv1

Description: Extract the second symbol from a length 4 string. (Contributed by Thierry Arnoux, 8-Oct-2020)

Ref Expression
Assertion s4fv1 
|- ( B e. V -> ( <" A B C D "> ` 1 ) = B )

Proof

Step Hyp Ref Expression
1 df-s4 
 |-  <" A B C D "> = ( <" A B C "> ++ <" D "> )
2 s3cli 
 |-  <" A B C "> e. Word _V
3 s3len 
 |-  ( # ` <" A B C "> ) = 3
4 s3fv1 
 |-  ( B e. V -> ( <" A B C "> ` 1 ) = B )
5 1nn0 
 |-  1 e. NN0
6 1lt3 
 |-  1 < 3
7 1 2 3 4 5 6 cats1fv 
 |-  ( B e. V -> ( <" A B C D "> ` 1 ) = B )