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Theorem afv2prc 45532
Description: A function's value at a proper class is not defined, compare with fvprc 6839. (Contributed by AV, 5-Sep-2022.)
Assertion
Ref Expression
afv2prc 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

Proof of Theorem afv2prc
StepHypRef Expression
1 prcnel 3471 . 2 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2 ndmafv2nrn 45528 . 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 2107  wnel 3050  Vcvv 3448  dom cdm 5638  ran crn 5639  ''''cafv2 45514
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-sep 5261  ax-pr 5389  ax-un 7677
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-nel 3051  df-rab 3411  df-v 3450  df-un 3920  df-in 3922  df-ss 3932  df-if 4492  df-pw 4567  df-sn 4592  df-pr 4594  df-uni 4871  df-dfat 45425  df-afv2 45515
This theorem is referenced by: (None)
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