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Theorem uniexd 39697
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 7072 . 2 (𝐴𝑉 𝐴 ∈ V)
31, 2syl 17 1 (𝜑 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2103  Vcvv 3304   cuni 4544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-8 2105  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704  ax-sep 4889  ax-un 7066
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-rex 3020  df-v 3306  df-uni 4545
This theorem is referenced by:  restuni4  39720  subsaluni  40998  issmflem  41359  issmflelem  41376  issmfle  41377  smfconst  41381  issmfgtlem  41387  issmfgt  41388  issmfgelem  41400  issmfge  41401  smfpimioo  41417  smfresal  41418
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