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Theorem unexd 7539
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 7534 . 2 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 587 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2110  Vcvv 3408  cun 3864
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708  ax-sep 5192  ax-nul 5199  ax-pr 5322  ax-un 7523
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3070  df-v 3410  df-dif 3869  df-un 3871  df-in 3873  df-ss 3883  df-nul 4238  df-sn 4542  df-pr 4544  df-uni 4820
This theorem is referenced by:  sexp2  33530  sexp3  33536  ssltun1  33739  ssltun2  33740  ofun  39924
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