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Metamath Proof Explorer

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	$⊢ Ord A \to A \subseteq suc ⋃ A$

Step	Hyp	Ref	Expression
1		ordsson	$⊢ Ord A \to A \subseteq On$
2		onsucuni	$⊢ A \subseteq On \to A \subseteq suc ⋃ A$
3	1 2	syl	$⊢ Ord A \to A \subseteq suc ⋃ A$