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Theorem limitssson 32531
Description: The class of all limit ordinals is a subclass of the class of all ordinals. (Contributed by Scott Fenton, 11-Apr-2012.)
Assertion
Ref Expression
limitssson Limits ⊆ On

Proof of Theorem limitssson
StepHypRef Expression
1 df-limits 32480 . 2 Limits = ((On ∩ Fix Bigcup ) ∖ {∅})
2 difss 3935 . . 3 ((On ∩ Fix Bigcup ) ∖ {∅}) ⊆ (On ∩ Fix Bigcup )
3 inss1 4028 . . 3 (On ∩ Fix Bigcup ) ⊆ On
42, 3sstri 3807 . 2 ((On ∩ Fix Bigcup ) ∖ {∅}) ⊆ On
51, 4eqsstri 3831 1 Limits ⊆ On
Colors of variables: wff setvar class
Syntax hints:  cdif 3766  cin 3768  wss 3769  c0 4115  {csn 4368  Oncon0 5941   Bigcup cbigcup 32454   Fix cfix 32455   Limits climits 32456
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-v 3387  df-dif 3772  df-in 3776  df-ss 3783  df-limits 32480
This theorem is referenced by: (None)
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