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Metamath Proof Explorer

Definition df-s3

Description: Define the length 3 word constructor. (Contributed by Mario Carneiro, 26-Feb-2016)

Ref Expression
Assertion df-s3 ⟨“ 𝐴 𝐵 𝐶 ”⟩ = ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA ⊢ 𝐴
1 cB ⊢ 𝐵
2 cC ⊢ 𝐶
3 0 1 2 cs3 ⊢ ⟨“ 𝐴 𝐵 𝐶 ”⟩
4 0 1 cs2 ⊢ ⟨“ 𝐴 𝐵 ”⟩
5 cconcat ⊢ ++
6 2 cs1 ⊢ ⟨“ 𝐶 ”⟩
7 4 6 5 co ⊢ ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )
8 3 7 wceq ⊢ ⟨“ 𝐴 𝐵 𝐶 ”⟩ = ( ⟨“ 𝐴 𝐵 ”⟩ ++ ⟨“ 𝐶 ”⟩ )