Theorem ontr

Description: An ordinal number is a transitive class. (Contributed by NM, 11-Jun-1994) Put in closed form. (Resised by BJ, 28-Dec-2024.)

	Ref	Expression
Assertion	ontr	⊢ ( 𝐴 ∈ On → Tr 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		eloni	⊢ ( 𝐴 ∈ On → Ord 𝐴 )
2		ordtr	⊢ ( Ord 𝐴 → Tr 𝐴 )
3	1 2	syl	⊢ ( 𝐴 ∈ On → Tr 𝐴 )