Theorem pwex 4271

Description: Power set axiom expressed in class notation. (Contributed by NM, 21-Jun-1993.)

Hypothesis

Ref	Expression
pwex.1	|- A e. _V

Assertion

Ref	Expression
pwex	|- ~P A e. _V

Proof of Theorem pwex

Step	Hyp	Ref	Expression
1		pwex.1	. 2 |- A e. _V
2		pwexg 4268	. 2 |- ( A e. _V -> ~P A e. _V )
3	1, 2	ax-mp 5	1 |- ~P A e. _V

Syntax hints:   e. wcel 2200   _Vcvv 2800   ~Pcpw 3650

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-14 2203  ax-ext 2211  ax-sep 4205  ax-pow 4262

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2802  df-in 3204  df-ss 3211  df-pw 3652

This theorem is referenced by:  p0ex  4276  pp0ex  4277  ord3ex  4278  abexssex  6282  fnpm  6820  exmidpw  7093  pw1on  7434  pw1dom2  7435  pw1nel3  7439  sucpw1ne3  7440  sucpw1nel3  7441  npex  7683  axcnex  8069  pnfxr  8222  mnfxr  8226  ixxex  10124  prdsvallem  13345  istopon  14727  dmtopon  14737  fncld  14812  pw1map  16532  pw1mapen  16533