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Theorem unexd 7741
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 7736 . 2 ((𝐴𝑉𝐵𝑊) → (𝐴𝐵) ∈ V)
41, 2, 3syl2anc 585 1 (𝜑 → (𝐴𝐵) ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3475  cun 3947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5428  ax-un 7725
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-sn 4630  df-pr 4632  df-uni 4910
This theorem is referenced by:  sexp2  8132  sexp3  8139  ssltun1  27309  ssltun2  27310  addsproplem2  27454  addsuniflem  27484  ssltmul1  27602  ssltmul2  27603  precsexlem11  27663  elrspunsn  32547  ofun  41058  tfsconcatun  42087  rclexi  42366  rtrclexlem  42367  trclubgNEW  42369  cnvrcl0  42376  dfrtrcl5  42380  iunrelexp0  42453  relexpmulg  42461  relexp01min  42464
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