Theorem pwex 4273

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 4270	. 2 |- ( A e. _V -> ~P A e. _V )
3	1, 2	ax-mp 5	1 |- ~P A e. _V

Syntax hints:   e. wcel 2202   _Vcvv 2802   ~Pcpw 3652

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-14 2205  ax-ext 2213  ax-sep 4207  ax-pow 4264

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-in 3206  df-ss 3213  df-pw 3654

This theorem is referenced by:  p0ex  4278  pp0ex  4279  ord3ex  4280  abexssex  6286  fnpm  6824  exmidpw  7099  pw1on  7443  pw1dom2  7444  pw1nel3  7448  sucpw1ne3  7449  sucpw1nel3  7450  npex  7692  axcnex  8078  pnfxr  8231  mnfxr  8235  ixxex  10133  prdsvallem  13354  istopon  14736  dmtopon  14746  fncld  14821  pw1map  16596  pw1mapen  16597