Theorem s3fv0

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

	Ref	Expression
Assertion	s3fv0	$$⊢A\in V\to ⟨“ABC”⟩\left(0\right)=A$$

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		s2fv0	$$⊢A\in V\to ⟨“AB”⟩\left(0\right)=A$$
5		0nn0	$$⊢0\in {\mathbb{N}}_0$$
6		2pos	$$⊢0<2$$
7	1 2 3 4 5 6	cats1fv	$$⊢A\in V\to ⟨“ABC”⟩\left(0\right)=A$$