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Theorem fixssrn 34424
Description: The fixpoints of a class are a subset of its range. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
fixssrn Fix 𝐴 ⊆ ran 𝐴

Proof of Theorem fixssrn
StepHypRef Expression
1 dffix2 34422 . 2 Fix 𝐴 = ran (𝐴 ∩ I )
2 inss1 4187 . . 3 (𝐴 ∩ I ) ⊆ 𝐴
32rnssi 5894 . 2 ran (𝐴 ∩ I ) ⊆ ran 𝐴
41, 3eqsstri 3977 1 Fix 𝐴 ⊆ ran 𝐴
Colors of variables: wff setvar class
Syntax hints:  cin 3908  wss 3909   I cid 5529  ran crn 5633   Fix cfix 34352
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2709  ax-sep 5255  ax-nul 5262  ax-pr 5383
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2816  df-ral 3064  df-rex 3073  df-rab 3407  df-v 3446  df-dif 3912  df-un 3914  df-in 3916  df-ss 3926  df-nul 4282  df-if 4486  df-sn 4586  df-pr 4588  df-op 4592  df-br 5105  df-opab 5167  df-id 5530  df-xp 5638  df-rel 5639  df-cnv 5640  df-dm 5642  df-rn 5643  df-fix 34376
This theorem is referenced by: (None)
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