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Theorem fixssdm 32138
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 32091 . 2 Fix 𝐴 = dom (𝐴 ∩ I )
2 inss1 3866 . . 3 (𝐴 ∩ I ) ⊆ 𝐴
3 dmss 5355 . . 3 ((𝐴 ∩ I ) ⊆ 𝐴 → dom (𝐴 ∩ I ) ⊆ dom 𝐴)
42, 3ax-mp 5 . 2 dom (𝐴 ∩ I ) ⊆ dom 𝐴
51, 4eqsstri 3668 1 Fix 𝐴 ⊆ dom 𝐴
Colors of variables: wff setvar class
Syntax hints:  cin 3606  wss 3607   I cid 5052  dom cdm 5143   Fix cfix 32067
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-dm 5153  df-fix 32091
This theorem is referenced by: (None)
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