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Theorem fixssdm 33481
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 33434 . 2 Fix 𝐴 = dom (𝐴 ∩ I )
2 inss1 4158 . . 3 (𝐴 ∩ I ) ⊆ 𝐴
3 dmss 5739 . . 3 ((𝐴 ∩ I ) ⊆ 𝐴 → dom (𝐴 ∩ I ) ⊆ dom 𝐴)
42, 3ax-mp 5 . 2 dom (𝐴 ∩ I ) ⊆ dom 𝐴
51, 4eqsstri 3952 1 Fix 𝐴 ⊆ dom 𝐴
Colors of variables: wff setvar class
Syntax hints:  cin 3883  wss 3884   I cid 5427  dom cdm 5523   Fix cfix 33410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-nfc 2941  df-v 3446  df-un 3889  df-in 3891  df-ss 3901  df-sn 4529  df-pr 4531  df-op 4535  df-br 5034  df-dm 5533  df-fix 33434
This theorem is referenced by: (None)
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