Theorem ordsucuni

Description: An ordinal class is a subclass of the successor of its union. (Contributed by NM, 12-Sep-2003)

	Ref	Expression
Assertion	ordsucuni	$$⊢\mathrm{Ord}A\to A\subseteq \mathrm{suc}\bigcup A$$

Proof

Step	Hyp	Ref	Expression
1		ordsson	$$⊢\mathrm{Ord}A\to A\subseteq \mathrm{On}$$
2		onsucuni	$$⊢A\subseteq \mathrm{On}\to A\subseteq \mathrm{suc}\bigcup A$$
3	1 2	syl	$$⊢\mathrm{Ord}A\to A\subseteq \mathrm{suc}\bigcup A$$