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| Mirrors > Home > ILE Home > Th. List > df-ot | GIF version | ||
| Description: Define ordered triple of classes. Definition of ordered triple in [Stoll] p. 25. (Contributed by NM, 3-Apr-2015.) | 
| Ref | Expression | 
|---|---|
| df-ot | ⊢ 〈𝐴, 𝐵, 𝐶〉 = 〈〈𝐴, 𝐵〉, 𝐶〉 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | cA | . . 3 class 𝐴 | |
| 2 | cB | . . 3 class 𝐵 | |
| 3 | cC | . . 3 class 𝐶 | |
| 4 | 1, 2, 3 | cotp 3626 | . 2 class 〈𝐴, 𝐵, 𝐶〉 | 
| 5 | 1, 2 | cop 3625 | . . 3 class 〈𝐴, 𝐵〉 | 
| 6 | 5, 3 | cop 3625 | . 2 class 〈〈𝐴, 𝐵〉, 𝐶〉 | 
| 7 | 4, 6 | wceq 1364 | 1 wff 〈𝐴, 𝐵, 𝐶〉 = 〈〈𝐴, 𝐵〉, 𝐶〉 | 
| Colors of variables: wff set class | 
| This definition is referenced by: oteq1 3817 oteq2 3818 oteq3 3819 otexg 4263 otth 4275 fnotovb 5965 ot1stg 6210 ot2ndg 6211 ot3rdgg 6212 ottposg 6313 | 
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