Theorem onuniorsuc

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) Put in closed form. (Revised by BJ, 11-Jan-2025)

	Ref	Expression
Assertion	onuniorsuc	|- ( A e. On -> ( A = U. A \/ A = suc U. A ) )

Proof

Step	Hyp	Ref	Expression
1		eloni	|- ( A e. On -> Ord A )
2		orduniorsuc	|- ( Ord A -> ( A = U. A \/ A = suc U. A ) )
3	1 2	syl	|- ( A e. On -> ( A = U. A \/ A = suc U. A ) )