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Definition df-pw 3862
 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 , then ~P ={ ,{3},{5},{7},{3,5}, {3,7},{5,7},{3,5,7}} (ex-pw 23636). We will later introduce the Axiom of Power Sets ax-pow 4470, which can be expressed in class notation per pwexg 4476. Still later we will prove, in hashpw 12198, 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, 24-Jun-1993.)
Assertion
Ref Expression
df-pw
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-pw
StepHypRef Expression
1 cA . . 3
21cpw 3860 . 2
3 vx . . . . 5
43cv 1368 . . . 4
54, 1wss 3328 . . 3
65, 3cab 2429 . 2
72, 6wceq 1369 1
 Colors of variables: wff setvar class This definition is referenced by:  pweq  3863  elpw  3866  nfpw  3872  pw0  4020  pwpw0  4021  pwsn  4085  pwsnALT  4086  pwex  4475  abssexg  4477  orduniss2  6444  mapex  7220  ssenen  7485  domtriomlem  8611  npex  9155  ustval  19777  avril1  23656  dfon2lem2  27597
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