Theorem onuni

Description: The union of an ordinal number is an ordinal number. (Contributed by NM, 29-Sep-2006)

	Ref	Expression
Assertion	onuni	$$⊢A\in \mathrm{On}\to \bigcup A\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		onss	$$⊢A\in \mathrm{On}\to A\subseteq \mathrm{On}$$
2		ssonuni	$$⊢A\in \mathrm{On}\to \left(A\subseteq \mathrm{On}\to \bigcup A\in \mathrm{On}\right)$$
3	1 2	mpd	$$⊢A\in \mathrm{On}\to \bigcup A\in \mathrm{On}$$