Metamath Proof Explorer


Definition df-on

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 }

Detailed syntax breakdown

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 }