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Theorem limitssson 29723
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 29671 . 2  |-  Limits  =  ( ( On  i^i  Fix Bigcup )  \  { (/) } )
2 difss 3627 . . 3  |-  ( ( On  i^i  Fix Bigcup ) 
\  { (/) } ) 
C_  ( On  i^i  Fix Bigcup )
3 inss1 3714 . . 3  |-  ( On 
i^i  Fix Bigcup )  C_  On
42, 3sstri 3508 . 2  |-  ( ( On  i^i  Fix Bigcup ) 
\  { (/) } ) 
C_  On
51, 4eqsstri 3529 1  |-  Limits  C_  On
Colors of variables: wff setvar class
Syntax hints:    \ cdif 3468    i^i cin 3470    C_ wss 3471   (/)c0 3793   {csn 4032   Oncon0 4887   Bigcupcbigcup 29645   Fixcfix 29646   Limitsclimits 29647
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3474  df-in 3478  df-ss 3485  df-limits 29671
This theorem is referenced by: (None)
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