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Theorem limord 4132
Description: A limit ordinal is ordinal. (Contributed by NM, 4-May-1995.)
Assertion
Ref Expression
limord  |-  ( Lim 
A  ->  Ord  A )

Proof of Theorem limord
StepHypRef Expression
1 dflim2 4107 . 2  |-  ( Lim 
A  <->  ( Ord  A  /\  (/)  e.  A  /\  A  =  U. A ) )
21simp1bi 919 1  |-  ( Lim 
A  ->  Ord  A )
Colors of variables: wff set class
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
This theorem depends on definitions:  df-bi 110  df-3an 887  df-ilim 4106
This theorem is referenced by:  limelon  4136  nlimsucg  4290
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