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Theorem bj-sselpwuni 36585
Description: Quantitative version of ssexg 5318: 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 5318 . 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 394  wcel 2098  Vcvv 3463  wss 3940  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 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696  ax-sep 5294
This theorem depends on definitions:  df-bi 206  df-an 395  df-3an 1086  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rab 3420  df-v 3465  df-in 3947  df-ss 3957  df-pw 4600  df-uni 4904
This theorem is referenced by:  bj-unirel  36586
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