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Theorem elpwi2OLD 5215
 Description: Obsolete version of elpwi2 5214 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 5212 . . 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 2111   ⊆ wss 3881  𝒫 cpw 4497 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-sep 5168 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-rab 3115  df-v 3443  df-in 3888  df-ss 3898  df-pw 4499 This theorem is referenced by: (None)
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