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Theorem afv2prc 43722
 Description: A function's value at a proper class is not defined, compare with fvprc 6645. (Contributed by AV, 5-Sep-2022.)
Assertion
Ref Expression
afv2prc 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

Proof of Theorem afv2prc
StepHypRef Expression
1 prcnel 3493 . 2 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2 ndmafv2nrn 43718 . 2 𝐴 ∈ dom 𝐹 → (𝐹''''𝐴) ∉ ran 𝐹)
31, 2syl 17 1 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2114   ∉ wnel 3115  Vcvv 3469  dom cdm 5532  ran crn 5533  ''''cafv2 43704 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794  ax-sep 5179  ax-nul 5186  ax-pr 5307  ax-un 7446 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-nel 3116  df-rab 3139  df-v 3471  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4266  df-if 4440  df-pw 4513  df-sn 4540  df-pr 4542  df-uni 4814  df-dfat 43615  df-afv2 43705 This theorem is referenced by: (None)
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