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Definition df-pw 3353
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  _V. 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 is { 3 , 5 , 7 }, then 
~P is { (/) , { 3 } , { 5 } , { 7 } , { 3 , 5 } , { 3 , 7 } , { 5 , 7 } , { 3 , 5 , 7 } }. We will later introduce the Axiom of Power Sets. Still later we will prove 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  ~P  {  | 
C_  }
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-pw
StepHypRef Expression
1 cA . . 3
21cpw 3351 . 2  ~P
3 vx . . . . 5  setvar
43cv 1241 . . . 4
54, 1wss 2911 . . 3  C_
65, 3cab 2023 . 2  {  |  C_  }
72, 6wceq 1242 1  ~P  {  | 
C_  }
Colors of variables: wff set class
This definition is referenced by:  pweq  3354  elpw  3357  nfpw  3363  pwss  3366  pw0  3502  snsspw  3526  pwsnss  3565  pwex  3923  abssexg  3925  iunpw  4177  iotass  4827  bdcpw  9324
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