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Theorem limuni 5946
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 df-lim 5889 . 2 (Lim 𝐴 ↔ (Ord 𝐴𝐴 ≠ ∅ ∧ 𝐴 = 𝐴))
21simp3bi 1142 1 (Lim 𝐴𝐴 = 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1632  wne 2932  c0 4058   cuni 4588  Ord word 5883  Lim wlim 5885
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 385  df-3an 1074  df-lim 5889
This theorem is referenced by:  limuni2  5947  unizlim  6005  nlimsucg  7208  oa0r  7789  om1r  7794  oarec  7813  oeworde  7844  oeeulem  7852  infeq5i  8708  r1sdom  8812  rankxplim3  8919  cflm  9284  coflim  9295  cflim2  9297  cfss  9299  cfslbn  9301  limsucncmpi  32771
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