Metamath Proof Explorer


Definition df-ot

Description: Define ordered triple of classes. Definition of ordered triple in Stoll p. 25. (Contributed by NM, 3-Apr-2015)

Ref Expression
Assertion df-ot ⟨ 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 cotp ⊢ ⟨ 𝐴 , 𝐵 , 𝐶 ⟩
4 0 1 cop ⊢ ⟨ 𝐴 , 𝐵 ⟩
5 4 2 cop ⊢ ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩
6 3 5 wceq ⊢ ⟨ 𝐴 , 𝐵 , 𝐶 ⟩ = ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩