Metamath Proof Explorer

Theorem s3fv0

Description: Extract the first symbol from a length 3 string. (Contributed by Mario Carneiro, 13-Jan-2017)

Ref Expression
Assertion s3fv0 
|- ( A e. V -> ( <" A B C "> ` 0 ) = A )

Proof

Step Hyp Ref Expression
1 df-s3 
 |-  <" A B C "> = ( <" A B "> ++ <" C "> )
2 s2cli 
 |-  <" A B "> e. Word _V
3 s2len 
 |-  ( # ` <" A B "> ) = 2
4 s2fv0 
 |-  ( A e. V -> ( <" A B "> ` 0 ) = A )
5 0nn0 
 |-  0 e. NN0
6 2pos 
 |-  0 < 2
7 1 2 3 4 5 6 cats1fv 
 |-  ( A e. V -> ( <" A B C "> ` 0 ) = A )