Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-on | Structured version Visualization version GIF version |
Description: Define the class of all ordinal numbers. Definition 7.11 of [TakeutiZaring] p. 38. (Contributed by NM, 5-Jun-1994.) |
Ref | Expression |
---|---|
df-on | ⊢ On = {𝑥 ∣ Ord 𝑥} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con0 6263 | . 2 class On | |
2 | vx | . . . . 5 setvar 𝑥 | |
3 | 2 | cv 1540 | . . . 4 class 𝑥 |
4 | 3 | word 6262 | . . 3 wff Ord 𝑥 |
5 | 4, 2 | cab 2716 | . 2 class {𝑥 ∣ Ord 𝑥} |
6 | 1, 5 | wceq 1541 | 1 wff On = {𝑥 ∣ Ord 𝑥} |
Colors of variables: wff setvar class |
This definition is referenced by: elong 6271 dfon2 33747 |
Copyright terms: Public domain | W3C validator |