Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-pw Unicode version

Definition df-pw 3361
 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 3359 . 2
3 vx . . . . 5
43cv 1242 . . . 4
54, 1wss 2917 . . 3
65, 3cab 2026 . 2
72, 6wceq 1243 1
 Colors of variables: wff set class This definition is referenced by:  pweq  3362  elpw  3365  nfpw  3371  pwss  3374  pw0  3511  snsspw  3535  pwsnss  3574  pwex  3932  abssexg  3934  iunpw  4211  iotass  4884  bdcpw  9989
 Copyright terms: Public domain W3C validator