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Metamath Proof Explorer

Theorem elong

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

		Ref	Expression
	Assertion	elong	$⊢ A \in V \to (A \in On \leftrightarrow Ord A)$

Step	Hyp	Ref	Expression
1		ordeq	$⊢ x = A \to (Ord x \leftrightarrow Ord A)$
2		df-on	$⊢ On = \{x \| Ord x\}$
3	1 2	elab2g	$⊢ A \in V \to (A \in On \leftrightarrow Ord A)$