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Theorem nfunsnafv 38043
 Description: If the restriction of a class to a singleton is not a function, its value is the universe, compare with nfunsn 5912 (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
nfunsnafv '''

Proof of Theorem nfunsnafv
StepHypRef Expression
1 df-dfat 38017 . . . 4 defAt
21simprbi 465 . . 3 defAt
32con3i 140 . 2 defAt
4 afvnfundmuv 38040 . 2 defAt '''
53, 4syl 17 1 '''
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1437   wcel 1870  cvv 3087  csn 4002   cdm 4854   cres 4856   wfun 5595   defAt wdfat 38014  '''cafv 38015 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 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-rab 2791  df-v 3089  df-un 3447  df-if 3916  df-fv 5609  df-dfat 38017  df-afv 38018 This theorem is referenced by:  afvvfunressn  38044  nfunsnaov  38087
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