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Theorem unexd 7636
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 7631 . 2 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 585 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2104  Vcvv 3437  cun 3890
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2707  ax-sep 5232  ax-nul 5239  ax-pr 5361  ax-un 7620
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 846  df-tru 1542  df-fal 1552  df-ex 1780  df-sb 2066  df-clab 2714  df-cleq 2728  df-clel 2814  df-rab 3287  df-v 3439  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-sn 4566  df-pr 4568  df-uni 4845
This theorem is referenced by:  sexp2  33838  sexp3  33844  ssltun1  34047  ssltun2  34048  ofun  40248
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