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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 )