Theorem s4fv2

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

	Ref	Expression
Assertion	s4fv2	$$⊢C\in V\to ⟨“ABCD”⟩\left(2\right)=C$$

Proof

Step	Hyp	Ref	Expression
1		df-s4	$$⊢⟨“ABCD”⟩=⟨“ABC”⟩\mathrm{++}⟨“D”⟩$$
2		s3cli	$$⊢⟨“ABC”⟩\in \mathrm{Word}\mathrm{V}$$
3		s3len	$$⊢\left|⟨“ABC”⟩\right|=3$$
4		s3fv2	$$⊢C\in V\to ⟨“ABC”⟩\left(2\right)=C$$
5		2nn0	$$⊢2\in {\mathbb{N}}_0$$
6		2lt3	$$⊢2<3$$
7	1 2 3 4 5 6	cats1fv	$$⊢C\in V\to ⟨“ABCD”⟩\left(2\right)=C$$