Theorem afv2prc 47996

Description: A function's value at a proper class is not defined, compare with fvprc 6877. (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 3482	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2		ndmafv2nrn 47992	. 2 ⊢ (¬ 𝐴 ∈ dom 𝐹 → (𝐹''''𝐴) ∉ ran 𝐹)
3	1, 2	syl 18	1 ⊢ (¬ 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∈ wcel 2146   ∉ wnel 3066  Vcvv 3457  dom cdm 5663  ran crn 5664  ''''cafv2 47978

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-sep 5259

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-nel 3067  df-rab 3419  df-v 3459  df-in 3913  df-ss 3923  df-if 4490  df-pw 4566  df-uni 4875  df-dfat 47889  df-afv2 47979

This theorem is used by: (None)