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Theorem fexafv2ex 45526
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 (𝐹𝑉 → (𝐹''''𝐴) ∈ V)

Proof of Theorem fexafv2ex
StepHypRef Expression
1 rnexg 7846 . 2 (𝐹𝑉 → ran 𝐹 ∈ V)
2 afv2ex 45520 . 2 (ran 𝐹 ∈ V → (𝐹''''𝐴) ∈ V)
31, 2syl 17 1 (𝐹𝑉 → (𝐹''''𝐴) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3448  ran crn 5639  ''''cafv2 45514
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-sep 5261  ax-nul 5268  ax-pow 5325  ax-pr 5389  ax-un 7677
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ne 2945  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-pw 4567  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-opab 5173  df-cnv 5646  df-dm 5648  df-rn 5649  df-iota 6453  df-afv2 45515
This theorem is referenced by: (None)
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