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Theorem fexafv2ex 46500
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 7892 . 2 (𝐹𝑉 → ran 𝐹 ∈ V)
2 afv2ex 46494 . 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 2098  Vcvv 3468  ran crn 5670  ''''cafv2 46488
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pow 5356  ax-pr 5420  ax-un 7722
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ne 2935  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-pw 4599  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-opab 5204  df-cnv 5677  df-dm 5679  df-rn 5680  df-iota 6489  df-afv2 46489
This theorem is referenced by: (None)
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