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Theorem fixssdm 25743
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 25695 . 2  |-  Fix A  =  dom  ( A  i^i  _I  )
2 inss1 3553 . . 3  |-  ( A  i^i  _I  )  C_  A
3 dmss 5061 . . 3  |-  ( ( A  i^i  _I  )  C_  A  ->  dom  ( A  i^i  _I  )  C_  dom  A )
42, 3ax-mp 8 . 2  |-  dom  ( A  i^i  _I  )  C_  dom  A
51, 4eqsstri 3370 1  |-  Fix A  C_ 
dom  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3311    C_ wss 3312    _I cid 4485   dom cdm 4870   Fixcfix 25671
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 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-dm 4880  df-fix 25695
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