Metamath Proof Explorer

Theorem ordtr

Description: An ordinal class is transitive. (Contributed by NM, 3-Apr-1994)

Ref Expression
Assertion ordtr ⊢ Ord ⁡ A → Tr ⁡ A

Proof

Step Hyp Ref Expression
1 df-ord ⊢ Ord ⁡ A ↔ Tr ⁡ A ∧ E We A
2 1 simplbi ⊢ Ord ⁡ A → Tr ⁡ A