Mathbox for Scott Fenton < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dffix2 Unicode version

Theorem dffix2 25663
 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 equid 1684 . . . . 5
2 vex 2923 . . . . . 6
3 breq1 4179 . . . . . . 7
4 equequ1 1692 . . . . . . 7
53, 4anbi12d 692 . . . . . 6
62, 5spcev 3007 . . . . 5
71, 6mpan2 653 . . . 4
83biimpac 473 . . . . 5
98exlimiv 1641 . . . 4
107, 9impbii 181 . . 3
112elfix 25661 . . 3
122elrn 5073 . . . 4
13 brin 4223 . . . . . 6
142ideq 4988 . . . . . . 7
1514anbi2i 676 . . . . . 6
1613, 15bitri 241 . . . . 5
1716exbii 1589 . . . 4
1812, 17bitri 241 . . 3
1910, 11, 183bitr4i 269 . 2
2019eqriv 2405 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1547   wceq 1649   wcel 1721   cin 3283   class class class wbr 4176   cid 4457   crn 4842  cfix 25596 This theorem is referenced by:  fixssrn  25665 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 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294  ax-nul 4302  ax-pr 4367 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 2262  df-mo 2263  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-ral 2675  df-rex 2676  df-rab 2679  df-v 2922  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-br 4177  df-opab 4231  df-id 4462  df-xp 4847  df-rel 4848  df-cnv 4849  df-dm 4851  df-rn 4852  df-fix 25618
 Copyright terms: Public domain W3C validator