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Theorem bj-sselpwuni 37051
Description: Quantitative version of ssexg 5323: 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 5323 . 2 ((𝐴𝐵𝐵𝑉) → 𝐴 ∈ V)
2 ssuni 4932 . 2 ((𝐴𝐵𝐵𝑉) → 𝐴 𝑉)
31, 2elpwd 4606 1 ((𝐴𝐵𝐵𝑉) → 𝐴 ∈ 𝒫 𝑉)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wcel 2108  Vcvv 3480  wss 3951  𝒫 cpw 4600   cuni 4907
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 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-sep 5296
This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-in 3958  df-ss 3968  df-pw 4602  df-uni 4908
This theorem is referenced by:  bj-unirel  37052
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