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Metamath Proof Explorer

Theorem elon

Description: An ordinal number is an ordinal set. (Contributed by NM, 5-Jun-1994)

		Ref	Expression
	Hypothesis	elon.1	$⊢ A \in V$
	Assertion	elon	$⊢ A \in On \leftrightarrow Ord A$

Step	Hyp	Ref	Expression
1		elon.1	$⊢ A \in V$
2		elong	$⊢ A \in V \to (A \in On \leftrightarrow Ord A)$
3	1 2	ax-mp	$⊢ A \in On \leftrightarrow Ord A$