Description: Extract the third symbol from a length 4 string. (Contributed by Thierry Arnoux, 8-Oct-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | s4fv2 | ⊢ ( 𝐶 ∈ 𝑉 → ( 〈“ 𝐴 𝐵 𝐶 𝐷 ”〉 ‘ 2 ) = 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-s4 | ⊢ 〈“ 𝐴 𝐵 𝐶 𝐷 ”〉 = ( 〈“ 𝐴 𝐵 𝐶 ”〉 ++ 〈“ 𝐷 ”〉 ) | |
2 | s3cli | ⊢ 〈“ 𝐴 𝐵 𝐶 ”〉 ∈ Word V | |
3 | s3len | ⊢ ( ♯ ‘ 〈“ 𝐴 𝐵 𝐶 ”〉 ) = 3 | |
4 | s3fv2 | ⊢ ( 𝐶 ∈ 𝑉 → ( 〈“ 𝐴 𝐵 𝐶 ”〉 ‘ 2 ) = 𝐶 ) | |
5 | 2nn0 | ⊢ 2 ∈ ℕ0 | |
6 | 2lt3 | ⊢ 2 < 3 | |
7 | 1 2 3 4 5 6 | cats1fv | ⊢ ( 𝐶 ∈ 𝑉 → ( 〈“ 𝐴 𝐵 𝐶 𝐷 ”〉 ‘ 2 ) = 𝐶 ) |