Theorem 0ellim 4543

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 4515	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp2bi 1044	1 |- ( Lim A -> (/) e. A )

This proof depends on syntax axioms:   -> wi 4   = wceq 1402   e. wcel 2209   (/)c0 3520   U.cuni 3935   Ord word 4507   Lim wlim 4509

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117  df-3an 1011  df-ilim 4514

This theorem is used by: (None)