Theorem onuniorsuci

Description: An ordinal number is either its own union (if zero or a limit ordinal) or the successor of its union. (Contributed by NM, 13-Jun-1994)

	Ref	Expression
Hypothesis	onssi.1	|- A e. On
Assertion	onuniorsuci	|- ( A = U. A \/ A = suc U. A )

Proof

Step	Hyp	Ref	Expression
1		onssi.1	|- A e. On
2	1	onordi	|- Ord A
3		orduniorsuc	|- ( Ord A -> ( A = U. A \/ A = suc U. A ) )
4	2 3	ax-mp	|- ( A = U. A \/ A = suc U. A )