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Theorem pwex 4107
Description: Power set axiom expressed in class notation. (Contributed by NM, 21-Jun-1993.)
Hypothesis
Ref Expression
pwex.1 𝐴 ∈ V
Assertion
Ref Expression
pwex 𝒫 𝐴 ∈ V

Proof of Theorem pwex
StepHypRef Expression
1 pwex.1 . 2 𝐴 ∈ V
2 pwexg 4104 . 2 (𝐴 ∈ V → 𝒫 𝐴 ∈ V)
31, 2ax-mp 5 1 𝒫 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1480  Vcvv 2686  𝒫 cpw 3510
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-in 3077  df-ss 3084  df-pw 3512
This theorem is referenced by:  p0ex  4112  pp0ex  4113  ord3ex  4114  abexssex  6023  fnpm  6550  exmidpw  6802  npex  7288  axcnex  7674  pnfxr  7825  mnfxr  7829  ixxex  9689  istopon  12189  dmtopon  12199  fncld  12276  pw1dom2  13243
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