Theorem ssonunii

Description: The union of a set of ordinal numbers is an ordinal number. Corollary 7N(d) of Enderton p. 193. (Contributed by NM, 20-Sep-2003)

	Ref	Expression
Hypothesis	ssonuni.1	$$⊢A\in \mathrm{V}$$
Assertion	ssonunii	$$⊢A\subseteq \mathrm{On}\to \bigcup A\in \mathrm{On}$$

Proof

Step	Hyp	Ref	Expression
1		ssonuni.1	$$⊢A\in \mathrm{V}$$
2		ssonuni	$$⊢A\in \mathrm{V}\to \left(A\subseteq \mathrm{On}\to \bigcup A\in \mathrm{On}\right)$$
3	1 2	ax-mp	$$⊢A\subseteq \mathrm{On}\to \bigcup A\in \mathrm{On}$$