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Theorem 0ellim 4101
Description: A limit ordinal contains the empty set. (Contributed by NM, 15-May-1994.)
Assertion
Ref Expression
0ellim (Lim A → ∅ A)

Proof of Theorem 0ellim
StepHypRef Expression
1 dflim2 4073 . 2 (Lim A ↔ (Ord A A A = A))
21simp2bi 919 1 (Lim A → ∅ A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  c0 3218   cuni 3571  Ord word 4065  Lim wlim 4067
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100
This theorem depends on definitions:  df-bi 110  df-3an 886  df-ilim 4072
This theorem is referenced by: (None)
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