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Theorem fv2prc 6951
Description: A function value of a function value at a proper class is the empty set. (Contributed by AV, 8-Apr-2021.)
Assertion
Ref Expression
fv2prc 𝐴 ∈ V → ((𝐹𝐴)‘𝐵) = ∅)

Proof of Theorem fv2prc
StepHypRef Expression
1 fvprc 6898 . . 3 𝐴 ∈ V → (𝐹𝐴) = ∅)
21fveq1d 6908 . 2 𝐴 ∈ V → ((𝐹𝐴)‘𝐵) = (∅‘𝐵))
3 0fv 6950 . 2 (∅‘𝐵) = ∅
42, 3eqtrdi 2793 1 𝐴 ∈ V → ((𝐹𝐴)‘𝐵) = ∅)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1540  wcel 2108  Vcvv 3480  c0 4333  cfv 6561
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-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-nf 1784  df-sb 2065  df-mo 2540  df-eu 2569  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-dm 5695  df-iota 6514  df-fv 6569
This theorem is referenced by:  elfv2ex  6952  itunitc1  10460  sralem  21175  sralemOLD  21176  srasca  21183  srascaOLD  21184  sravsca  21185  sravscaOLD  21186  sraip  21187
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