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Theorem limuni2 6291
Description: The union of a limit ordinal is a limit ordinal. (Contributed by NM, 19-Sep-2006.)
Assertion
Ref Expression
limuni2 (Lim 𝐴 → Lim 𝐴)

Proof of Theorem limuni2
StepHypRef Expression
1 limuni 6290 . . 3 (Lim 𝐴𝐴 = 𝐴)
2 limeq 6242 . . 3 (𝐴 = 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
31, 2syl 17 . 2 (Lim 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
43ibi 270 1 (Lim 𝐴 → Lim 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209   = wceq 1543   cuni 4833  Lim wlim 6231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-ext 2709
This theorem depends on definitions:  df-bi 210  df-an 400  df-3an 1091  df-tru 1546  df-ex 1788  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-ne 2942  df-ral 3067  df-v 3422  df-in 3887  df-ss 3897  df-uni 4834  df-tr 5176  df-po 5482  df-so 5483  df-fr 5523  df-we 5525  df-ord 6233  df-lim 6235
This theorem is referenced by:  rankxplim2  9520  rankxplim3  9521
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