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Theorem uniexd 38310
Description: Deduction version of the ZF Axiom of Union in class notation. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
uniexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
uniexd (𝜑 𝐴 ∈ V)

Proof of Theorem uniexd
StepHypRef Expression
1 uniexd.1 . 2 (𝜑𝐴𝑉)
2 uniexg 6853 . 2 (𝐴𝑉 𝐴 ∈ V)
31, 2syl 17 1 (𝜑 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 1977  Vcvv 3173   cuni 4372
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-un 6847
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-v 3175  df-uni 4373
This theorem is referenced by:  restuni4  38336  subsaluni  39254  issmflem  39613  issmfltle  39622  issmflelem  39631  issmfle  39632  smfconst  39636  issmfgtlem  39642  issmfgt  39643  issmfgelem  39655  issmfge  39656  smfpimioo  39672  smfresal  39673
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