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Theorem 0ellim 4189
Description: A limit ordinal contains the empty set. (Contributed by NM, 15-May-1994.)
Assertion
Ref Expression
0ellim  |-  ( Lim 
A  ->  (/)  e.  A
)

Proof of Theorem 0ellim
StepHypRef Expression
1 dflim2 4161 . 2  |-  ( Lim 
A  <->  ( Ord  A  /\  (/)  e.  A  /\  A  =  U. A ) )
21simp2bi 955 1  |-  ( Lim 
A  ->  (/)  e.  A
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    e. wcel 1434   (/)c0 3269   U.cuni 3627   Ord word 4153   Lim wlim 4155
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-3an 922  df-ilim 4160
This theorem is referenced by: (None)
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