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Theorem limord 4407
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 4382 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp1bi 1013 1 (Lim 𝐴 → Ord 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1363  wcel 2158  c0 3434   cuni 3821  Ord word 4374  Lim wlim 4376
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106
This theorem depends on definitions:  df-bi 117  df-3an 981  df-ilim 4381
This theorem is referenced by:  limelon  4411  nlimsucg  4577
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