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Theorem fvclex 7941
Description: Existence of the class of values of a set. (Contributed by NM, 9-Nov-1995.)
Hypothesis
Ref Expression
fvclex.1 𝐹 ∈ V
Assertion
Ref Expression
fvclex {𝑦 ∣ ∃𝑥 𝑦 = (𝐹𝑥)} ∈ V
Distinct variable group:   𝑥,𝑦,𝐹

Proof of Theorem fvclex
StepHypRef Expression
1 fvclex.1 . . . 4 𝐹 ∈ V
21rnex 7899 . . 3 ran 𝐹 ∈ V
3 snex 5424 . . 3 {∅} ∈ V
42, 3unex 7729 . 2 (ran 𝐹 ∪ {∅}) ∈ V
5 fvclss 7235 . 2 {𝑦 ∣ ∃𝑥 𝑦 = (𝐹𝑥)} ⊆ (ran 𝐹 ∪ {∅})
64, 5ssexi 5315 1 {𝑦 ∣ ∃𝑥 𝑦 = (𝐹𝑥)} ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wex 1773  wcel 2098  {cab 2703  Vcvv 3468  cun 3941  c0 4317  {csn 4623  ran crn 5670  cfv 6536
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-10 2129  ax-11 2146  ax-12 2163  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420  ax-un 7721
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-nf 1778  df-sb 2060  df-mo 2528  df-eu 2557  df-clab 2704  df-cleq 2718  df-clel 2804  df-ne 2935  df-ral 3056  df-rex 3065  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-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 6488  df-fv 6544
This theorem is referenced by:  fvresex  7942
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