Theorem afv2prc 47353

Description: A function's value at a proper class is not defined, compare with fvprc 6822. (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 3463	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2		ndmafv2nrn 47349	. 2 ⊢ (¬ 𝐴 ∈ dom 𝐹 → (𝐹''''𝐴) ∉ ran 𝐹)
3	1, 2	syl 17	1 ⊢ (¬ 𝐴 ∈ V → (𝐹''''𝐴) ∉ ran 𝐹)

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2113   ∉ wnel 3033  Vcvv 3437  dom cdm 5621  ran crn 5622  ''''cafv2 47335

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-sep 5238  ax-pr 5374  ax-un 7676

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-nel 3034  df-rab 3397  df-v 3439  df-un 3903  df-in 3905  df-ss 3915  df-if 4477  df-pw 4553  df-sn 4578  df-pr 4580  df-uni 4861  df-dfat 47246  df-afv2 47336

This theorem is referenced by: (None)