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Theorem elfix 25460
 Description: Membership in the fixpoints of a class. (Contributed by Scott Fenton, 11-Apr-2012.)
Hypothesis
Ref Expression
elfix.1
Assertion
Ref Expression
elfix

Proof of Theorem elfix
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-fix 25417 . . 3
21eleq2i 2444 . 2
3 elfix.1 . . . 4
43eldm 5000 . . 3
5 brin 4193 . . . . . 6
6 vex 2895 . . . . . . . 8
76ideq 4958 . . . . . . 7
87anbi2i 676 . . . . . 6
95, 8bitri 241 . . . . 5
109exbii 1589 . . . 4
11 breq2 4150 . . . . . . 7
1211biimparc 474 . . . . . 6
1312exlimiv 1641 . . . . 5
14 eqid 2380 . . . . . 6
15 breq2 4150 . . . . . . . 8
16 eqeq2 2389 . . . . . . . 8
1715, 16anbi12d 692 . . . . . . 7
183, 17spcev 2979 . . . . . 6
1914, 18mpan2 653 . . . . 5
2013, 19impbii 181 . . . 4
2110, 20bitri 241 . . 3
224, 21bitri 241 . 2
232, 22bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1547   wceq 1649   wcel 1717  cvv 2892   cin 3255   class class class wbr 4146   cid 4427   cdm 4811  cfix 25395 This theorem is referenced by:  elfix2  25461  dffix2  25462  fixcnv  25465  ellimits  25467  elfuns  25471  dfrdg4  25506  tfrqfree  25507 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361  ax-sep 4264  ax-nul 4272  ax-pr 4337 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235  df-mo 2236  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rex 2648  df-rab 2651  df-v 2894  df-dif 3259  df-un 3261  df-in 3263  df-ss 3270  df-nul 3565  df-if 3676  df-sn 3756  df-pr 3757  df-op 3759  df-br 4147  df-opab 4201  df-id 4432  df-xp 4817  df-rel 4818  df-dm 4821  df-fix 25417
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