Theorem limord 4542

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 4517	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp1bi 1043	1 |- ( Lim A -> Ord A )

This proof depends on syntax axioms:   -> wi 4   = wceq 1402   e. wcel 2209   (/)c0 3520   U.cuni 3935   Ord word 4509   Lim wlim 4511

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

This proof depends on definitions:  df-bi 117  df-3an 1011  df-ilim 4516

This theorem is used by:  limelon  4546  nlimsucg  4715