Theorem s3fv2

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

	Ref	Expression
Assertion	s3fv2	⊢ ( 𝐶 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 𝐶 ”⟩ ‘ 2 ) = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		df-s3	⊢ ⟨“ 𝐴 𝐵 𝐶 ”⟩ = ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )
2		s2cli	⊢ ⟨“ 𝐴 𝐵 ”⟩ ∈ Word V
3		s2len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 ”⟩ ) = 2
4	1 2 3	cats1fvn	⊢ ( 𝐶 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 𝐶 ”⟩ ‘ 2 ) = 𝐶 )