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Definition df-pw 3839
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 ~PA={ ,{3},{5},{7},{3,5}, {3,7},{5,7},{3,5,7}} (ex-pw 23315). We will later introduce the Axiom of Power Sets ax-pow 4442, which can be expressed in class notation per pwexg 4448. Still later we will prove, in hashpw 12139, 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 3837 . 2
3 vx . . . . 5
43cv 1686 . . . 4
54, 1wss 3305 . . 3
65, 3cab 2408 . 2
72, 6wceq 1687 1
Colors of variables: wff setvar class
This definition is referenced by:  pweq  3840  elpw  3843  nfpw  3849  pw0  3995  pwpw0  3996  pwsn  4060  pwsnALT  4061  pwex  4447  abssexg  4449  orduniss2  6414  mapex  7181  ssenen  7444  domtriomlem  8558  npex  9101  ustval  19477  avril1  23335  dfon2lem2  27299
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