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Theorem pwexd 4073
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 4072 . 2 (𝐴𝑉 → 𝒫 𝐴 ∈ V)
31, 2syl 14 1 (𝜑 → 𝒫 𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1463  Vcvv 2658  𝒫 cpw 3478
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-sep 4014  ax-pow 4066
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-in 3045  df-ss 3052  df-pw 3480
This theorem is referenced by:  fival  6824  toponsspwpwg  12084  tgvalex  12114  cnpfval  12259  blfvalps  12449
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