Metamath Proof Explorer


Theorem s6cli

Description: A length 6 string is a word. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion s6cli ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ∈ Word V

Proof

Step Hyp Ref Expression
1 df-s6 ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ++ ⟨“ 𝐹 ”⟩ )
2 s5cli ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ∈ Word V
3 1 2 cats1cli ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ”⟩ ∈ Word V