Theorem pwid 4024

Description: A set is a member of its power class. Theorem 87 of [Suppes] p. 47. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
pwid.1	|- A e. _V

Assertion

Ref	Expression
pwid	|- A e. ~P A

Proof of Theorem pwid

Step	Hyp	Ref	Expression
1		pwid.1	. 2 |- A e. _V
2		pwidg 4023	. 2 |- ( A e. _V -> A e. ~P A )
3	1, 2	ax-mp 5	1 |- A e. ~P A

Syntax hints:   e. wcel 1767   _Vcvv 3113   ~Pcpw 4010

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483  df-ss 3490  df-pw 4012

This theorem is referenced by:  r1ordg  8192  rankr1id  8276  cfss  8641  0ram  14393  evl1fval1lem  18137  bastg  19234  fincmp  19659  restlly  19750  ptbasfi  19817  zfbas  20132  ustfilxp  20450  metustfbasOLD  20803  metustfbas  20804  minveclem3b  21578  wilthlem3  23072  coinflipprob  28058  pwtrrVD  32705  mapdunirnN  36447