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Theorem limitssson 27964
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 27912 . 2  |-  Limits  =  ( ( On  i^i  Fix Bigcup )  \  { (/) } )
2 difss 3504 . . 3  |-  ( ( On  i^i  Fix Bigcup ) 
\  { (/) } ) 
C_  ( On  i^i  Fix Bigcup )
3 inss1 3591 . . 3  |-  ( On 
i^i  Fix Bigcup )  C_  On
42, 3sstri 3386 . 2  |-  ( ( On  i^i  Fix Bigcup ) 
\  { (/) } ) 
C_  On
51, 4eqsstri 3407 1  |-  Limits  C_  On
Colors of variables: wff setvar class
Syntax hints:    \ cdif 3346    i^i cin 3348    C_ wss 3349   (/)c0 3658   {csn 3898   Oncon0 4740   Bigcupcbigcup 27886   Fixcfix 27887   Limitsclimits 27888
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-v 2995  df-dif 3352  df-in 3356  df-ss 3363  df-limits 27912
This theorem is referenced by: (None)
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