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Theorem afvvdm 27983
 Description: If the function value of a class for an argument is a set, the argument is contained in the domain of the class. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
afvvdm '''

Proof of Theorem afvvdm
StepHypRef Expression
1 ndmafv 27982 . . 3 '''
2 nvelim 27956 . . 3 ''' '''
31, 2syl 16 . 2 '''
43con4i 125 1 '''
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1653   wcel 1726  cvv 2958   cdm 4880  '''cafv 27950 This theorem is referenced by:  aovvdm  28027  aovrcl  28031  aoprssdm  28044 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332 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 5464  df-dfat 27952  df-afv 27953
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