Metamath Proof Explorer


Theorem onordi

Description: An ordinal number is an ordinal class. (Contributed by NM, 11-Jun-1994)

Ref Expression
Hypothesis on.1 ⊢ A ∈ On
Assertion onordi ⊢ Ord ⁡ A

Proof

Step Hyp Ref Expression
1 on.1 ⊢ A ∈ On
2 eloni ⊢ A ∈ On → Ord ⁡ A
3 1 2 ax-mp ⊢ Ord ⁡ A