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Theorem fixssdm 24517
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 24471 . 2  |-  Fix A  =  dom  ( A  i^i  _I  )
2 inss1 3402 . . 3  |-  ( A  i^i  _I  )  C_  A
3 dmss 4894 . . 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 3221 1  |-  Fix A  C_ 
dom  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3164    C_ wss 3165    _I cid 4320   dom cdm 4705   Fixcfix 24449
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-dm 4715  df-fix 24471
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