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Theorem elpwi2OLD 5240
Description: Obsolete version of elpwi2 5239 as of 26-May-2024. (Contributed by Glauco Siliprandi, 3-Mar-2021.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
elpwi2.1 𝐵𝑉
elpwi2.2 𝐴𝐵
Assertion
Ref Expression
elpwi2OLD 𝐴 ∈ 𝒫 𝐵

Proof of Theorem elpwi2OLD
StepHypRef Expression
1 elpwi2.2 . 2 𝐴𝐵
2 elpwi2.1 . . 3 𝐵𝑉
3 elpw2g 5237 . . 3 (𝐵𝑉 → (𝐴 ∈ 𝒫 𝐵𝐴𝐵))
42, 3ax-mp 5 . 2 (𝐴 ∈ 𝒫 𝐵𝐴𝐵)
51, 4mpbir 234 1 𝐴 ∈ 𝒫 𝐵
Colors of variables: wff setvar class
Syntax hints:  wb 209  wcel 2110  wss 3866  𝒫 cpw 4513
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708  ax-sep 5192
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3070  df-v 3410  df-in 3873  df-ss 3883  df-pw 4515
This theorem is referenced by: (None)
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