Theorem ontrci

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

	Ref	Expression
Hypothesis	on.1	$$⊢A\in \mathrm{On}$$
Assertion	ontrci	$$⊢\mathrm{Tr}A$$

Proof

Step	Hyp	Ref	Expression
1		on.1	$$⊢A\in \mathrm{On}$$
2	1	onordi	$$⊢\mathrm{Ord}A$$
3		ordtr	$$⊢\mathrm{Ord}A\to \mathrm{Tr}A$$
4	2 3	ax-mp	$$⊢\mathrm{Tr}A$$