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 )