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Theorem limuni2 6245
 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 6244 . . 3 (Lim 𝐴𝐴 = 𝐴)
2 limeq 6196 . . 3 (𝐴 = 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
31, 2syl 17 . 2 (Lim 𝐴 → (Lim 𝐴 ↔ Lim 𝐴))
43ibi 269 1 (Lim 𝐴 → Lim 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 208   = wceq 1530  ∪ cuni 4830  Lim wlim 6185 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2791 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1083  df-tru 1533  df-ex 1774  df-nf 1778  df-sb 2063  df-clab 2798  df-cleq 2812  df-clel 2891  df-ne 3015  df-ral 3141  df-rex 3142  df-in 3941  df-ss 3950  df-uni 4831  df-tr 5164  df-po 5467  df-so 5468  df-fr 5507  df-we 5509  df-ord 6187  df-lim 6189 This theorem is referenced by:  rankxplim2  9301  rankxplim3  9302
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