Theorem limord 4430

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

Assertion

Ref	Expression
limord	|- ( Lim A -> Ord A )

Proof of Theorem limord

Step	Hyp	Ref	Expression
1		dflim2 4405	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp1bi 1014	1 |- ( Lim A -> Ord A )

Syntax hints:   -> wi 4   = wceq 1364   e. wcel 2167   (/)c0 3450   U.cuni 3839   Ord word 4397   Lim wlim 4399

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

This theorem depends on definitions:  df-bi 117  df-3an 982  df-ilim 4404

This theorem is referenced by:  limelon  4434  nlimsucg  4602