Theorem s4fv3

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

	Ref	Expression
Assertion	s4fv3	⊢ ( 𝐷 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ‘ 3 ) = 𝐷 )

Proof

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	1 2 3	cats1fvn	⊢ ( 𝐷 ∈ 𝑉 → ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ‘ 3 ) = 𝐷 )