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Theorem limuni 4379
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 4353 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp3bi 1009 1 (Lim 𝐴𝐴 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1348  wcel 2141  c0 3414   cuni 3794  Ord word 4345  Lim wlim 4347
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 975  df-ilim 4352
This theorem is referenced by:  limuni2  4380  nlimsucg  4548  freccllem  6378  frecfcllem  6380  frecsuclem  6382
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