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Theorem pwex 4183
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 4180 . 2 (𝐴 ∈ V → 𝒫 𝐴 ∈ V)
31, 2ax-mp 5 1 𝒫 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2148  Vcvv 2737  𝒫 cpw 3575
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-14 2151  ax-ext 2159  ax-sep 4121  ax-pow 4174
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135  df-ss 3142  df-pw 3577
This theorem is referenced by:  p0ex  4188  pp0ex  4189  ord3ex  4190  abexssex  6125  fnpm  6655  exmidpw  6907  pw1on  7224  pw1dom2  7225  pw1nel3  7229  sucpw1ne3  7230  sucpw1nel3  7231  npex  7471  axcnex  7857  pnfxr  8009  mnfxr  8013  ixxex  9898  istopon  13449  dmtopon  13459  fncld  13534
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