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Theorem dffix2 25755
 Description: The fixpoints of a class in terms of its range. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
dffix2

Proof of Theorem dffix2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 2961 . . . 4
21elfix 25753 . . 3
31elrn 5113 . . . 4
4 brin 4262 . . . . . 6
5 ancom 439 . . . . . 6
61ideq 5028 . . . . . . 7
76anbi1i 678 . . . . . 6
84, 5, 73bitri 264 . . . . 5
98exbii 1593 . . . 4
10 breq1 4218 . . . . 5
111, 10ceqsexv 2993 . . . 4
123, 9, 113bitri 264 . . 3
132, 12bitr4i 245 . 2
1413eqriv 2435 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wceq 1653   wcel 1726   cin 3321   class class class wbr 4215   cid 4496   crn 4882  cfix 25684 This theorem is referenced by:  fixssrn  25757 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4216  df-opab 4270  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-dm 4891  df-rn 4892  df-fix 25708
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