This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 0ellim

Description: A limit ordinal contains the empty set. (Contributed by NM, 15-May-1994)

		Ref	Expression
	Assertion	0ellim	$⊢ Lim A \to \emptyset \in A$

Step	Hyp	Ref	Expression
1		dflim2	$⊢ Lim A \leftrightarrow (Ord A \land \emptyset \in A \land A = ⋃ A)$
2	1	simp2bi	$⊢ Lim A \to \emptyset \in A$