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Theorem limitssson 33851
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 33800 . 2 Limits = ((On ∩ Fix Bigcup ) ∖ {∅})
2 difss 4022 . . 3 ((On ∩ Fix Bigcup ) ∖ {∅}) ⊆ (On ∩ Fix Bigcup )
3 inss1 4119 . . 3 (On ∩ Fix Bigcup ) ⊆ On
42, 3sstri 3886 . 2 ((On ∩ Fix Bigcup ) ∖ {∅}) ⊆ On
51, 4eqsstri 3911 1 Limits ⊆ On
Colors of variables: wff setvar class
Syntax hints:  cdif 3840  cin 3842  wss 3843  c0 4211  {csn 4516  Oncon0 6172   Bigcup cbigcup 33774   Fix cfix 33775   Limits climits 33776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-8 2116  ax-9 2124  ax-ext 2710
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-ex 1787  df-sb 2075  df-clab 2717  df-cleq 2730  df-clel 2811  df-v 3400  df-dif 3846  df-in 3850  df-ss 3860  df-limits 33800
This theorem is referenced by: (None)
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