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Theorem afv2prc 42129
 Description: A function's value at a proper class is not defined, compare with fvprc 6427. (Contributed by AV, 5-Sep-2022.)
Assertion
Ref Expression
afv2prc 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

Proof of Theorem afv2prc
StepHypRef Expression
1 prcnel 3436 . 2 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2 ndmafv2nrn 42125 . 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 2166   ∉ wnel 3103  Vcvv 3415  dom cdm 5343  ran crn 5344  ''''cafv2 42111 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-8 2168  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2804  ax-sep 5006  ax-nul 5014  ax-pr 5128  ax-un 7210 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2813  df-cleq 2819  df-clel 2822  df-nfc 2959  df-nel 3104  df-rex 3124  df-rab 3127  df-v 3417  df-dif 3802  df-un 3804  df-in 3806  df-ss 3813  df-nul 4146  df-if 4308  df-pw 4381  df-sn 4399  df-pr 4401  df-uni 4660  df-dfat 42022  df-afv2 42112 This theorem is referenced by: (None)
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