Description: Define the class of all ordinal numbers. Definition 7.11 of TakeutiZaring p. 38. (Contributed by NM, 5-Jun-1994)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | df-on | ⊢ On = { 𝑥 ∣ Ord 𝑥 } |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 0 | con0 | ⊢ On | |
| 1 | vx | ⊢ 𝑥 | |
| 2 | 1 | cv | ⊢ 𝑥 |
| 3 | 2 | word | ⊢ Ord 𝑥 |
| 4 | 3 1 | cab | ⊢ { 𝑥 ∣ Ord 𝑥 } |
| 5 | 0 4 | wceq | ⊢ On = { 𝑥 ∣ Ord 𝑥 } |