Theorem 0ellim 4315

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

Assertion

Ref	Expression
0ellim	|- ( Lim A -> (/) e. A )

Proof of Theorem 0ellim

Step	Hyp	Ref	Expression
1		dflim2 4287	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp2bi 997	1 |- ( Lim A -> (/) e. A )

Syntax hints:   -> wi 4   = wceq 1331   e. wcel 1480   (/)c0 3358   U.cuni 3731   Ord word 4279   Lim wlim 4281

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-3an 964  df-ilim 4286

This theorem is referenced by: (None)