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Theorem limuni 4190
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 4164 . 2 (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴𝐴 = 𝐴))
21simp3bi 958 1 (Lim 𝐴𝐴 = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  wcel 1436  c0 3272   cuni 3630  Ord word 4156  Lim wlim 4158
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 924  df-ilim 4163
This theorem is referenced by:  limuni2  4191  nlimsucg  4348  freccllem  6102  frecfcllem  6104  frecsuclem  6106
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