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Metamath Proof Explorer

Theorem onss

Description: An ordinal number is a subset of the class of ordinal numbers. (Contributed by NM, 5-Jun-1994)

		Ref	Expression
	Assertion	onss	$⊢ A \in On \to A \subseteq On$

Step	Hyp	Ref	Expression
1		eloni	$⊢ A \in On \to Ord A$
2		ordsson	$⊢ Ord A \to A \subseteq On$
3	1 2	syl	$⊢ A \in On \to A \subseteq On$