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Theorem limord 4357
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 4332 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp1bi 997 1 (Lim 𝐴 → Ord 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1335  wcel 2128  c0 3395   cuni 3774  Ord word 4324  Lim wlim 4326
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-3an 965  df-ilim 4331
This theorem is referenced by:  limelon  4361  nlimsucg  4527
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