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Definition df-pw 3724
 Description: Define power class. Definition 5.10 of [TakeutiZaring] p. 17, but we also let it apply to proper classes, i.e. those that are not members of . When applied to a set, this produces its power set. A power set of S is the set of all subsets of S, including the empty set and S itself. For example, if 3 , 5 , 7 , then 3 5 7 3 , 5 3 , 7 5 , 7 3 , 5 , 7 (ex-pw in set.mm). We will later introduce the Axiom of Power Sets ax-pow in set.mm, which can be expressed in class notation per pwexg 4328. Still later we will prove, in hashpw in set.mm, that the size of the power set of a finite set is 2 raised to the power of the size of the set. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
df-pw
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-pw
StepHypRef Expression
1 cA . . 3
21cpw 3722 . 2
3 vx . . . . 5
43cv 1641 . . . 4
54, 1wss 3257 . . 3
65, 3cab 2339 . 2
72, 6wceq 1642 1
 Colors of variables: wff setvar class This definition is referenced by:  pweq  3725  elpw  3728  nfpw  3733  pwss  3736  pwpw0  3855  snsspw  3877  pwsn  3881  pwsnALT  3882  pw0  4160  eqpwrelk  4478  srelk  4524  pmex  6005  pmvalg  6010  enpw1pw  6075
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