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Theorem limitssson 35912
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 35861 . 2 Limits = ((On ∩ Fix Bigcup ) ∖ {∅})
2 difss 4136 . . 3 ((On ∩ Fix Bigcup ) ∖ {∅}) ⊆ (On ∩ Fix Bigcup )
3 inss1 4237 . . 3 (On ∩ Fix Bigcup ) ⊆ On
42, 3sstri 3993 . 2 ((On ∩ Fix Bigcup ) ∖ {∅}) ⊆ On
51, 4eqsstri 4030 1 Limits ⊆ On
Colors of variables: wff setvar class
Syntax hints:  cdif 3948  cin 3950  wss 3951  c0 4333  {csn 4626  Oncon0 6384   Bigcup cbigcup 35835   Fix cfix 35836   Limits climits 35837
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-in 3958  df-ss 3968  df-limits 35861
This theorem is referenced by: (None)
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