Theorem s3len

Description: The length of a length 3 string. (Contributed by Mario Carneiro, 26-Feb-2016)

	Ref	Expression
Assertion	s3len	$$⊢\left|⟨“ABC”⟩\right|=3$$

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		2p1e3	$$⊢2+1=3$$
5	1 2 3 4	cats1len	$$⊢\left|⟨“ABC”⟩\right|=3$$