Metamath Proof Explorer


Theorem s5cli

Description: A length 5 string is a word. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion s5cli ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ∈ Word V

Proof

Step Hyp Ref Expression
1 df-s5 ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ = ( ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ++ ⟨“ 𝐸 ”⟩ )
2 s4cli ⟨“ 𝐴 𝐵 𝐶 𝐷 ”⟩ ∈ Word V
3 1 2 cats1cli ⟨“ 𝐴 𝐵 𝐶 𝐷 𝐸 ”⟩ ∈ Word V