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Definition df-pw 3512
 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 is { 3 , 5 , 7 }, then 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
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-pw
StepHypRef Expression
1 cA . . 3
21cpw 3510 . 2
3 vx . . . . 5
43cv 1330 . . . 4
54, 1wss 3071 . . 3
65, 3cab 2125 . 2
72, 6wceq 1331 1
 Colors of variables: wff set class This definition is referenced by:  pweq  3513  elpw  3516  nfpw  3523  pwss  3526  pw0  3667  snsspw  3691  pwsnss  3730  vpwex  4103  abssexg  4106  iunpw  4401  iotass  5105  mapex  6548  ssenen  6745  tgvalex  12233  bdcpw  13126
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