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Theorem unexd 39472
 Description: The union of two sets is a set. (Contributed by SN, 16-Jul-2024.)
Hypotheses
Ref Expression
unexd.1 (𝜑𝐴𝑉)
unexd.2 (𝜑𝐵𝑊)
Assertion
Ref Expression
unexd (𝜑 → (𝐴𝐵) ∈ V)

Proof of Theorem unexd
StepHypRef Expression
1 unexd.1 . 2 (𝜑𝐴𝑉)
2 unexd.2 . 2 (𝜑𝐵𝑊)
3 unexg 7462 . 2 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 587 1 (𝜑 → (𝐴𝐵) ∈ V)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∈ wcel 2111  Vcvv 3441   ∪ cun 3880 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-sep 5170  ax-nul 5177  ax-pr 5298  ax-un 7451 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-rab 3115  df-v 3443  df-dif 3885  df-un 3887  df-in 3889  df-ss 3899  df-nul 4246  df-sn 4528  df-pr 4530  df-uni 4804 This theorem is referenced by:  ofun  39485
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