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Metamath Proof Explorer

Theorem limord

Description: A limit ordinal is ordinal. (Contributed by NM, 4-May-1995)

		Ref	Expression
	Assertion	limord	$⊢ Lim A \to Ord A$

Step	Hyp	Ref	Expression
1		df-lim	$⊢ Lim A \leftrightarrow (Ord A \land A \neq \emptyset \land A = ⋃ A)$
2	1	simp1bi	$⊢ Lim A \to Ord A$