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Theorem limitssson 25756
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  C_  On

Proof of Theorem limitssson
StepHypRef Expression
1 df-limits 25704 . 2  |-  Limits  =  ( ( On  i^i  Fix Bigcup )  \  { (/) } )
2 difss 3474 . . 3  |-  ( ( On  i^i  Fix Bigcup ) 
\  { (/) } ) 
C_  ( On  i^i  Fix Bigcup )
3 inss1 3561 . . 3  |-  ( On 
i^i  Fix Bigcup )  C_  On
42, 3sstri 3357 . 2  |-  ( ( On  i^i  Fix Bigcup ) 
\  { (/) } ) 
C_  On
51, 4eqsstri 3378 1  |-  Limits  C_  On
Colors of variables: wff set class
Syntax hints:    \ cdif 3317    i^i cin 3319    C_ wss 3320   (/)c0 3628   {csn 3814   Oncon0 4581   Bigcupcbigcup 25678   Fixcfix 25679   Limitsclimits 25680
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-dif 3323  df-in 3327  df-ss 3334  df-limits 25704
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