Metamath Proof Explorer

Theorem oneli

Description: A member of an ordinal number is an ordinal number. Theorem 7M(a) of Enderton p. 192. (Contributed by NM, 11-Jun-1994)

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

Step	Hyp	Ref	Expression
1		on.1	$⊢ A \in On$
2		onelon	$⊢ (A \in On \land B \in A) \to B \in On$
3	1 2	mpan	$⊢ B \in A \to B \in On$