Theorem limuni 4541

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 4515	. 2 |- ( Lim A <-> ( Ord A /\ (/) e. A /\ A = U. A ) )
2	1	simp3bi 1045	1 |- ( Lim A -> A = U. 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  ax-ia3 108

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

This theorem is used by:  limuni2  4542  nlimsucg  4713  freccllem  6673  frecfcllem  6675  frecsuclem  6677