Theorem fexafv2ex 47249

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 7898	. 2 ⊢ (𝐹 ∈ 𝑉 → ran 𝐹 ∈ V)
2		afv2ex 47243	. 2 ⊢ (ran 𝐹 ∈ V → (𝐹''''𝐴) ∈ V)
3	1, 2	syl 17	1 ⊢ (𝐹 ∈ 𝑉 → (𝐹''''𝐴) ∈ V)

Syntax hints:   → wi 4   ∈ wcel 2108  Vcvv 3459  ran crn 5655  ''''cafv2 47237

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 2007  ax-8 2110  ax-9 2118  ax-ext 2707  ax-sep 5266  ax-nul 5276  ax-pow 5335  ax-pr 5402  ax-un 7729

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 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-ne 2933  df-rab 3416  df-v 3461  df-dif 3929  df-un 3931  df-in 3933  df-ss 3943  df-nul 4309  df-if 4501  df-pw 4577  df-sn 4602  df-pr 4604  df-op 4608  df-uni 4884  df-br 5120  df-opab 5182  df-cnv 5662  df-dm 5664  df-rn 5665  df-iota 6484  df-afv2 47238

This theorem is referenced by: (None)