Theorem limuni 4374

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 4348	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp3bi 1004	1 |- ( Lim A -> A = U. A )

Syntax hints:   -> wi 4   = wceq 1343   e. wcel 2136   (/)c0 3409   U.cuni 3789   Ord word 4340   Lim wlim 4342

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970  df-ilim 4347

This theorem is referenced by:  limuni2  4375  nlimsucg  4543  freccllem  6370  frecfcllem  6372  frecsuclem  6374