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Theorem fixssdm 24446
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 24400 . 2  |-  Fix A  =  dom  ( A  i^i  _I  )
2 inss1 3389 . . 3  |-  ( A  i^i  _I  )  C_  A
3 dmss 4878 . . 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 3208 1  |-  Fix A  C_ 
dom  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3151    C_ wss 3152    _I cid 4304   dom cdm 4689   Fixcfix 24378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-dm 4699  df-fix 24400
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