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Theorem fixssdm 29718
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 29670 . 2  |-  Fix A  =  dom  ( A  i^i  _I  )
2 inss1 3714 . . 3  |-  ( A  i^i  _I  )  C_  A
3 dmss 5212 . . 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 3529 1  |-  Fix A  C_ 
dom  A
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3470    C_ wss 3471    _I cid 4799   dom cdm 5008   Fixcfix 29646
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-br 4457  df-dm 5018  df-fix 29670
This theorem is referenced by: (None)
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