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Theorem limord 4186
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 4161 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp1bi 954 1 (Lim 𝐴 → Ord 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285  wcel 1434  c0 3269   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
This theorem depends on definitions:  df-bi 115  df-3an 922  df-ilim 4160
This theorem is referenced by:  limelon  4190  nlimsucg  4345
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