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Theorem limuni 4133
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 4107 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp3bi 921 1 (Lim 𝐴𝐴 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1243  wcel 1393  c0 3224   cuni 3580  Ord word 4099  Lim wlim 4101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887  df-ilim 4106
This theorem is referenced by:  limuni2  4134  nlimsucg  4290
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