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Theorem subfacval 29725
 Description: The subfactorial is defined as the number of derangements (see derangval 29719) of the set . (Contributed by Mario Carneiro, 21-Jan-2015.)
Hypotheses
Ref Expression
derang.d
subfac.n
Assertion
Ref Expression
subfacval
Distinct variable groups:   ,,,,   ,   ,,,
Allowed substitution hints:   (,,)   ()

Proof of Theorem subfacval
StepHypRef Expression
1 oveq2 6304 . . 3
21fveq2d 5876 . 2
3 subfac.n . 2
4 fvex 5882 . 2
52, 3, 4fvmpt 5955 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437   wcel 1867  cab 2405   wne 2616  wral 2773   cmpt 4475  wf1o 5591  cfv 5592  (class class class)co 6296  cfn 7568  c1 9529  cn0 10858  cfz 11771  chash 12501 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-sbc 3297  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4214  df-br 4418  df-opab 4476  df-mpt 4477  df-id 4760  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-iota 5556  df-fun 5594  df-fv 5600  df-ov 6299 This theorem is referenced by:  derangen2  29726  subfaclefac  29728  subfac0  29729  subfac1  29730  subfacp1lem6  29737
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