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Theorem fixssdm 35872
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 ⊆ dom 𝐴

Proof of Theorem fixssdm
StepHypRef Expression
1 df-fix 35825 . 2 Fix 𝐴 = dom (𝐴 ∩ I )
2 inss1 4258 . . 3 (𝐴 ∩ I ) ⊆ 𝐴
3 dmss 5927 . . 3 ((𝐴 ∩ I ) ⊆ 𝐴 → dom (𝐴 ∩ I ) ⊆ dom 𝐴)
42, 3ax-mp 5 . 2 dom (𝐴 ∩ I ) ⊆ dom 𝐴
51, 4eqsstri 4043 1 Fix 𝐴 ⊆ dom 𝐴
Colors of variables: wff setvar class
Syntax hints:  cin 3975  wss 3976   I cid 5592  dom cdm 5700   Fix cfix 35801
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-in 3983  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-br 5167  df-dm 5710  df-fix 35825
This theorem is referenced by: (None)
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