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Theorem uniexd 40040
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 7189 . 2 (𝐴𝑉 𝐴 ∈ V)
31, 2syl 17 1 (𝜑 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2157  Vcvv 3385   cuni 4628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-8 2159  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2777  ax-sep 4975  ax-un 7183
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-rex 3095  df-v 3387  df-uni 4629
This theorem is referenced by:  restuni4  40062  subsaluni  41321  issmflem  41682  issmflelem  41699  issmfle  41700  smfconst  41704  issmfgtlem  41710  issmfgt  41711  issmfgelem  41723  issmfge  41724  smfpimioo  41740  smfresal  41741
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