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Theorem limuni2 5824
 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 5823 . . 3 (Lim 𝐴𝐴 = 𝐴)
2 limeq 5773 . . 3 (𝐴 = 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
31, 2syl 17 . 2 (Lim 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
43ibi 256 1 (Lim 𝐴 → Lim 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196   = wceq 1523  ∪ cuni 4468  Lim wlim 5762 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-ral 2946  df-rex 2947  df-in 3614  df-ss 3621  df-uni 4469  df-tr 4786  df-po 5064  df-so 5065  df-fr 5102  df-we 5104  df-ord 5764  df-lim 5766 This theorem is referenced by:  rankxplim2  8781  rankxplim3  8782
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