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Theorem afvprc 47129
Description: A function's value at a proper class is the universe, compare with fvprc 6896. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
afvprc 𝐴 ∈ V → (𝐹'''𝐴) = V)

Proof of Theorem afvprc
StepHypRef Expression
1 prcnel 3506 . 2 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2 ndmafv 47125 . 2 𝐴 ∈ dom 𝐹 → (𝐹'''𝐴) = V)
31, 2syl 17 1 𝐴 ∈ V → (𝐹'''𝐴) = V)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1540  wcel 2108  Vcvv 3479  dom cdm 5683  '''cafv 47102
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707  ax-sep 5294  ax-nul 5304  ax-pr 5430
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2539  df-eu 2568  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-ne 2940  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-sbc 3788  df-csb 3899  df-dif 3953  df-un 3955  df-in 3957  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4625  df-pr 4627  df-op 4631  df-uni 4906  df-int 4945  df-br 5142  df-opab 5204  df-id 5576  df-xp 5689  df-rel 5690  df-cnv 5691  df-co 5692  df-dm 5693  df-res 5695  df-iota 6512  df-fun 6561  df-fv 6567  df-aiota 47070  df-dfat 47104  df-afv 47105
This theorem is referenced by:  afvvv  47130
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