Theorem afv2prc 47963

Description: A function's value at a proper class is not defined, compare with fvprc 6873. (Contributed by AV, 5-Sep-2022.)

Assertion

Ref	Expression
afv2prc	⊢ (¬ 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

Proof of Theorem afv2prc

Step	Hyp	Ref	Expression
1		prcnel 3480	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2		ndmafv2nrn 47959	. 2 ⊢ (¬ 𝐴 ∈ dom 𝐹 → (𝐹''''𝐴) ∉ ran 𝐹)
3	1, 2	syl 18	1 ⊢ (¬ 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2143   ∉ wnel 3064  Vcvv 3455  dom cdm 5661  ran crn 5662  ''''cafv2 47945

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5257

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-nel 3065  df-rab 3417  df-v 3457  df-in 3912  df-ss 3922  df-if 4488  df-pw 4564  df-uni 4873  df-dfat 47856  df-afv2 47946

This theorem is referenced by: (None)