Theorem s4fv3

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

	Ref	Expression
Assertion	s4fv3	$$⊢D\in V\to ⟨“ABCD”⟩\left(3\right)=D$$

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	1 2 3	cats1fvn	$$⊢D\in V\to ⟨“ABCD”⟩\left(3\right)=D$$