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Theorem fixssdm 25472
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 25426 . 2  |-  Fix A  =  dom  ( A  i^i  _I  )
2 inss1 3506 . . 3  |-  ( A  i^i  _I  )  C_  A
3 dmss 5011 . . 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 3323 1  |-  Fix A  C_ 
dom  A
Colors of variables: wff set class
Syntax hints:    i^i cin 3264    C_ wss 3265    _I cid 4436   dom cdm 4820   Fixcfix 25404
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-rab 2660  df-v 2903  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-br 4156  df-dm 4830  df-fix 25426
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