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Theorem fixssrn 29491
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  C_ 
ran  A

Proof of Theorem fixssrn
StepHypRef Expression
1 dffix2 29489 . 2  |-  Fix A  =  ran  ( A  i^i  _I  )
2 inss1 3723 . . 3  |-  ( A  i^i  _I  )  C_  A
3 rnss 5237 . . 3  |-  ( ( A  i^i  _I  )  C_  A  ->  ran  ( A  i^i  _I  )  C_  ran  A )
42, 3ax-mp 5 . 2  |-  ran  ( A  i^i  _I  )  C_  ran  A
51, 4eqsstri 3539 1  |-  Fix A  C_ 
ran  A
Colors of variables: wff setvar class
Syntax hints:    i^i cin 3480    C_ wss 3481    _I cid 4796   ran crn 5006   Fixcfix 29418
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-br 4454  df-opab 4512  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-dm 5015  df-rn 5016  df-fix 29442
This theorem is referenced by: (None)
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