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Theorem ndmafv 39869
 Description: The value of a class outside its domain is the universe, compare with ndmfv 6128. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
ndmafv 𝐴 ∈ dom 𝐹 → (𝐹'''𝐴) = V)

Proof of Theorem ndmafv
StepHypRef Expression
1 df-dfat 39845 . . . 4 (𝐹 defAt 𝐴 ↔ (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴})))
21simplbi 475 . . 3 (𝐹 defAt 𝐴𝐴 ∈ dom 𝐹)
32con3i 149 . 2 𝐴 ∈ dom 𝐹 → ¬ 𝐹 defAt 𝐴)
4 afvnfundmuv 39868 . 2 𝐹 defAt 𝐴 → (𝐹'''𝐴) = V)
53, 4syl 17 1 𝐴 ∈ dom 𝐹 → (𝐹'''𝐴) = V)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   = wceq 1475   ∈ wcel 1977  Vcvv 3173  {csn 4125  dom cdm 5038   ↾ cres 5040  Fun wfun 5798   defAt wdfat 39842  '''cafv 39843 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-un 3545  df-if 4037  df-fv 5812  df-dfat 39845  df-afv 39846 This theorem is referenced by:  afvvdm  39870  afvprc  39873  afvco2  39905  ndmaov  39912  aovprc  39917
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