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Theorem afvvfunressn 38515
 Description: If the function value of a class for an argument is a set, the class restricted to the singleton of the argument is a function. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
afvvfunressn '''

Proof of Theorem afvvfunressn
StepHypRef Expression
1 nfunsnafv 38514 . . 3 '''
2 nvelim 38492 . . 3 ''' '''
31, 2syl 17 . 2 '''
43con4i 133 1 '''
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wceq 1437   wcel 1872  cvv 3080  csn 3998   cres 4855   wfun 5595  '''cafv 38486 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-rab 2780  df-v 3082  df-un 3441  df-if 3912  df-fv 5609  df-dfat 38488  df-afv 38489 This theorem is referenced by:  aovvfunressn  38559
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