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Theorem ndmafv 40554
Description: The value of a class outside its domain is the universe, compare with ndmfv 6185. (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 40530 . . . 4 (𝐹 defAt 𝐴 ↔ (𝐴 ∈ dom 𝐹 ∧ Fun (𝐹 ↾ {𝐴})))
21simplbi 476 . . 3 (𝐹 defAt 𝐴𝐴 ∈ dom 𝐹)
32con3i 150 . 2 𝐴 ∈ dom 𝐹 → ¬ 𝐹 defAt 𝐴)
4 afvnfundmuv 40553 . 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 1480  wcel 1987  Vcvv 3190  {csn 4155  dom cdm 5084  cres 5086  Fun wfun 5851   defAt wdfat 40527  '''cafv 40528
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rab 2917  df-v 3192  df-un 3565  df-if 4065  df-fv 5865  df-dfat 40530  df-afv 40531
This theorem is referenced by:  afvvdm  40555  afvprc  40558  afvco2  40590  ndmaov  40597  aovprc  40602
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