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Theorem fixssdm 27959
Description: The fixpoints of a class are a subset of its domain. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
fixssdm  |-  Fix A  C_ 
dom  A

Proof of Theorem fixssdm
StepHypRef Expression
1 df-fix 27911 . 2  |-  Fix A  =  dom  ( A  i^i  _I  )
2 inss1 3591 . . 3  |-  ( A  i^i  _I  )  C_  A
3 dmss 5060 . . 3  |-  ( ( A  i^i  _I  )  C_  A  ->  dom  ( A  i^i  _I  )  C_  dom  A )
42, 3ax-mp 5 . 2  |-  dom  ( A  i^i  _I  )  C_  dom  A
51, 4eqsstri 3407 1  |-  Fix A  C_ 
dom  A
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3348    C_ wss 3349    _I cid 4652   dom cdm 4861   Fixcfix 27887
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-or 370  df-an 371  df-3an 967  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-rab 2745  df-v 2995  df-dif 3352  df-un 3354  df-in 3356  df-ss 3363  df-nul 3659  df-if 3813  df-sn 3899  df-pr 3901  df-op 3905  df-br 4314  df-dm 4871  df-fix 27911
This theorem is referenced by: (None)
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