Theorem fexafv2ex 47221

Description: The alternate function value is always a set if the function (resp. the domain of the function) is a set. (Contributed by AV, 3-Sep-2022.)

Assertion

Ref	Expression
fexafv2ex	⊢ (𝐹 ∈ 𝑉 → (𝐹''''𝐴) ∈ V)

Proof of Theorem fexafv2ex

Step	Hyp	Ref	Expression
1		rnexg 7878	. 2 ⊢ (𝐹 ∈ 𝑉 → ran 𝐹 ∈ V)
2		afv2ex 47215	. 2 ⊢ (ran 𝐹 ∈ V → (𝐹''''𝐴) ∈ V)
3	1, 2	syl 17	1 ⊢ (𝐹 ∈ 𝑉 → (𝐹''''𝐴) ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2109  Vcvv 3447  ran crn 5639  ''''cafv2 47209

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 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-sep 5251  ax-nul 5261  ax-pow 5320  ax-pr 5387  ax-un 7711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-ne 2926  df-rab 3406  df-v 3449  df-dif 3917  df-un 3919  df-in 3921  df-ss 3931  df-nul 4297  df-if 4489  df-pw 4565  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4872  df-br 5108  df-opab 5170  df-cnv 5646  df-dm 5648  df-rn 5649  df-iota 6464  df-afv2 47210

This theorem is referenced by: (None)