Theorem s3len

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

	Ref	Expression
Assertion	s3len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 ”⟩ ) = 3

Proof

Step	Hyp	Ref	Expression
1		df-s3	⊢ ⟨“ 𝐴 𝐵 𝐶 ”⟩ = ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )
2		s2cli	⊢ ⟨“ 𝐴 𝐵 ”⟩ ∈ Word V
3		s2len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 ”⟩ ) = 2
4		2p1e3	⊢ ( 2 + 1 ) = 3
5	1 2 3 4	cats1len	⊢ ( ♯ ‘ ⟨“ 𝐴 𝐵 𝐶 ”⟩ ) = 3