Theorem s3fv2

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

	Ref	Expression
Assertion	s3fv2	$$⊢C\in V\to ⟨“ABC”⟩\left(2\right)=C$$

Proof

Step	Hyp	Ref	Expression
1		df-s3	$$⊢⟨“ABC”⟩=⟨“AB”⟩\mathrm{++}⟨“C”⟩$$
2		s2cli	$$⊢⟨“AB”⟩\in \mathrm{Word}\mathrm{V}$$
3		s2len	$$⊢\left|⟨“AB”⟩\right|=2$$
4	1 2 3	cats1fvn	$$⊢C\in V\to ⟨“ABC”⟩\left(2\right)=C$$