Theorem onun2i

Description: The union of two ordinal numbers is an ordinal number. (Contributed by NM, 13-Jun-1994)

	Ref	Expression
Hypotheses	on.1	$$⊢A\in \mathrm{On}$$
	on.2	$$⊢B\in \mathrm{On}$$
Assertion	onun2i	$$⊢A\cup B\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		on.1	$$⊢A\in \mathrm{On}$$
2		on.2	$$⊢B\in \mathrm{On}$$
3		onun2	$$⊢\left(A\in \mathrm{On}\wedge B\in \mathrm{On}\right)\to A\cup B\in \mathrm{On}$$
4	1 2 3	mp2an	$$⊢A\cup B\in \mathrm{On}$$