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 } |