This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ A \in On \to (A = ⋃ A \lor A = suc ⋃ A)$

Proof

Step	Hyp	Ref	Expression
1		eloni	$⊢ A \in On \to Ord A$
2		orduniorsuc	$⊢ Ord A \to (A = ⋃ A \lor A = suc ⋃ A)$
3	1 2	syl	$⊢ A \in On \to (A = ⋃ A \lor A = suc ⋃ A)$