Theorem limuni 4133

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

Assertion

Ref	Expression
limuni	|- ( Lim A -> A = U. A )

Proof of Theorem limuni

Step	Hyp	Ref	Expression
1		dflim2 4107	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp3bi 921	1 |- ( Lim A -> A = U. A )

Syntax hints:   -> wi 4   = wceq 1243   e. wcel 1393   (/)c0 3224   U.cuni 3580   Ord word 4099   Lim wlim 4101

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887  df-ilim 4106

This theorem is referenced by:  limuni2  4134  nlimsucg  4290