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Metamath Proof Explorer

Theorem onelssi

Description: A member of an ordinal number is a subset of it. (Contributed by NM, 11-Aug-1994)

		Ref	Expression
	Hypothesis	on.1	$⊢ A \in On$
	Assertion	onelssi	$⊢ B \in A \to B \subseteq A$

Step	Hyp	Ref	Expression
1		on.1	$⊢ A \in On$
2		onelss	$⊢ A \in On \to (B \in A \to B \subseteq A)$
3	1 2	ax-mp	$⊢ B \in A \to B \subseteq A$