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Theorem bj-sselpwuni 36452
Description: Quantitative version of ssexg 5317: a subset of an element of a class is an element of the powerclass of the union of that class. (Contributed by BJ, 6-Apr-2024.)
Assertion
Ref Expression
bj-sselpwuni ((𝐴𝐵𝐵𝑉) → 𝐴 ∈ 𝒫 𝑉)

Proof of Theorem bj-sselpwuni
StepHypRef Expression
1 ssexg 5317 . 2 ((𝐴𝐵𝐵𝑉) → 𝐴 ∈ V)
2 ssuni 4930 . 2 ((𝐴𝐵𝐵𝑉) → 𝐴 𝑉)
31, 2elpwd 4604 1 ((𝐴𝐵𝐵𝑉) → 𝐴 ∈ 𝒫 𝑉)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wcel 2099  Vcvv 3469  wss 3944  𝒫 cpw 4598   cuni 4903
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698  ax-sep 5293
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3428  df-v 3471  df-in 3951  df-ss 3961  df-pw 4600  df-uni 4904
This theorem is referenced by:  bj-unirel  36453
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