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Theorem limuni 4325
Description: A limit ordinal is its own supremum (union). (Contributed by NM, 4-May-1995.)
Assertion
Ref Expression
limuni (Lim 𝐴𝐴 = 𝐴)

Proof of Theorem limuni
StepHypRef Expression
1 dflim2 4299 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp3bi 999 1 (Lim 𝐴𝐴 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1332  wcel 1481  c0 3367   cuni 3743  Ord word 4291  Lim wlim 4293
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965  df-ilim 4298
This theorem is referenced by:  limuni2  4326  nlimsucg  4488  freccllem  6306  frecfcllem  6308  frecsuclem  6310
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