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Metamath Proof Explorer

Theorem onuni

Description: The union of an ordinal number is an ordinal number. (Contributed by NM, 29-Sep-2006)

		Ref	Expression
	Assertion	onuni	$⊢ A \in On \to ⋃ A \in On$

Step	Hyp	Ref	Expression
1		onss	$⊢ A \in On \to A \subseteq On$
2		ssonuni	$⊢ A \in On \to (A \subseteq On \to ⋃ A \in On)$
3	1 2	mpd	$⊢ A \in On \to ⋃ A \in On$