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Theorem pwexd 5267
Description: Deduction version of the power set axiom. (Contributed by Glauco Siliprandi, 26-Jun-2021.)
Hypothesis
Ref Expression
pwexd.1 (𝜑𝐴𝑉)
Assertion
Ref Expression
pwexd (𝜑 → 𝒫 𝐴 ∈ V)

Proof of Theorem pwexd
StepHypRef Expression
1 pwexd.1 . 2 (𝜑𝐴𝑉)
2 pwexg 5266 . 2 (𝐴𝑉 → 𝒫 𝐴 ∈ V)
31, 2syl 17 1 (𝜑 → 𝒫 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2115  Vcvv 3480  𝒫 cpw 4521
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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-pow 5253
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-in 3926  df-ss 3936  df-pw 4523
This theorem is referenced by:  undefval  7932  mapex  8402  pmvalg  8407  fopwdom  8615  pwdom  8660  fineqvlem  8723  fival  8867  fipwuni  8881  hartogslem2  8998  wdompwdom  9033  harwdom  9046  canthwe  10065  canthp1lem2  10067  gchdjuidm  10082  gchpwdom  10084  gchhar  10093  prdsmulr  16728  sylow2a  18740  selvffval  20322  toponsspwpw  21523  mretopd  21693  ordtbaslem  21789  ptcmplem1  22653  isust  22805  blfvalps  22986  carsgval  31586  neibastop2lem  33733  bj-imdirvallem  34508  bj-imdirval2lem  34510  rfovcnvf1od  40559  fsovfd  40567  fsovcnvlem  40568  dssmapnvod  40575  dssmapf1od  40576  ntrneif1o  40634  ntrneicnv  40637  ntrneiel  40640  clsneiel1  40667  neicvgf1o  40673  neicvgnvo  40674  neicvgel1  40678  ntrelmap  40684  clselmap  40686  salexct  42837  psmeasurelem  42972  caragenval  42995  omeunile  43007  0ome  43031  isomennd  43033  afv2ex  43633
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