Theorem 0ellim 4153

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 4125	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp2bi 954	1 |- ( Lim A -> (/) e. A )

Syntax hints:   -> wi 4   = wceq 1284   e. wcel 1433   (/)c0 3251   U.cuni 3601   Ord word 4117   Lim wlim 4119

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem depends on definitions:  df-bi 115  df-3an 921  df-ilim 4124

This theorem is referenced by: (None)