Theorem s3fv1

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

	Ref	Expression
Assertion	s3fv1	$$⊢B\in V\to ⟨“ABC”⟩\left(1\right)=B$$

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		s2fv1	$$⊢B\in V\to ⟨“AB”⟩\left(1\right)=B$$
5		1nn0	$$⊢1\in {\mathbb{N}}_0$$
6		1lt2	$$⊢1<2$$
7	1 2 3 4 5 6	cats1fv	$$⊢B\in V\to ⟨“ABC”⟩\left(1\right)=B$$