Theorem afv2prc 43500

Description: A function's value at a proper class is not defined, compare with fvprc 6656. (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 3515	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2		ndmafv2nrn 43496	. 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 3122  Vcvv 3491  dom cdm 5548  ran crn 5549  ''''cafv2 43482

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2792  ax-sep 5196  ax-nul 5203  ax-pr 5323  ax-un 7454

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1084  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2799  df-cleq 2813  df-clel 2892  df-nfc 2962  df-nel 3123  df-rab 3146  df-v 3493  df-dif 3932  df-un 3934  df-in 3936  df-ss 3945  df-nul 4285  df-if 4461  df-pw 4534  df-sn 4561  df-pr 4563  df-uni 4832  df-dfat 43393  df-afv2 43483

This theorem is referenced by: (None)