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Theorem pwexd 4141
 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 4140 . 2 (𝐴𝑉 → 𝒫 𝐴 ∈ V)
31, 2syl 14 1 (𝜑 → 𝒫 𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 2128  Vcvv 2712  𝒫 cpw 3543 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4082  ax-pow 4134 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108  df-ss 3115  df-pw 3545 This theorem is referenced by:  fival  6907  toponsspwpwg  12380  tgvalex  12410  cnpfval  12555  blfvalps  12745
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