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Theorem nfunsnafv 27996
 Description: If the restriction of a class to a singleton is not a function, its value is the universe, compare with nfunsn 5764 (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
nfunsnafv '''

Proof of Theorem nfunsnafv
StepHypRef Expression
1 df-dfat 27964 . . . 4 defAt
21simprbi 452 . . 3 defAt
32con3i 130 . 2 defAt
4 afvnfundmuv 27993 . 2 defAt '''
53, 4syl 16 1 '''
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1653   wcel 1726  cvv 2958  csn 3816   cdm 4881   cres 4883   wfun 5451   defAt wdfat 27961  '''cafv 27962 This theorem is referenced by:  afvvfunressn  27997  nfunsnaov  28040 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-un 3327  df-if 3742  df-fv 5465  df-dfat 27964  df-afv 27965
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