Theorem afv2prc 47995

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 3483	. 2 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹)
2		ndmafv2nrn 47991	. 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 3067  Vcvv 3458  dom cdm 5664  ran crn 5665  ''''cafv2 47977

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 2738  ax-sep 5260

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 2745  df-cleq 2758  df-clel 2841  df-nel 3068  df-rab 3420  df-v 3460  df-in 3915  df-ss 3925  df-if 4491  df-pw 4567  df-uni 4876  df-dfat 47888  df-afv2 47978

This theorem is used by: (None)