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Theorem fexafv2ex 43729
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 7611 . 2 (𝐹𝑉 → ran 𝐹 ∈ V)
2 afv2ex 43723 . 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 2115  Vcvv 3480  ran crn 5544  ''''cafv2 43717
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5190  ax-nul 5197  ax-pow 5254  ax-pr 5318  ax-un 7457
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-rab 3142  df-v 3482  df-sbc 3759  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-pw 4524  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5054  df-opab 5116  df-cnv 5551  df-dm 5553  df-rn 5554  df-iota 6304  df-afv2 43718
This theorem is referenced by: (None)
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