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Definition df-igen 31739
Description: Define the ideal generated by a subset of a ring. (Contributed by Jeff Madsen, 10-Jun-2010.)
Assertion
Ref Expression
df-igen  |-  IdlGen  =  ( r  e.  RingOps ,  s  e.  ~P ran  ( 1st `  r )  |->  |^|
{ j  e.  ( Idl `  r )  |  s  C_  j } )
Distinct variable group:    s, r, j

Detailed syntax breakdown of Definition df-igen
StepHypRef Expression
1 cigen 31738 . 2  class  IdlGen
2 vr . . 3  setvar  r
3 vs . . 3  setvar  s
4 crngo 25791 . . 3  class  RingOps
52cv 1404 . . . . . 6  class  r
6 c1st 6782 . . . . . 6  class  1st
75, 6cfv 5569 . . . . 5  class  ( 1st `  r )
87crn 4824 . . . 4  class  ran  ( 1st `  r )
98cpw 3955 . . 3  class  ~P ran  ( 1st `  r )
103cv 1404 . . . . . 6  class  s
11 vj . . . . . . 7  setvar  j
1211cv 1404 . . . . . 6  class  j
1310, 12wss 3414 . . . . 5  wff  s  C_  j
14 cidl 31686 . . . . . 6  class  Idl
155, 14cfv 5569 . . . . 5  class  ( Idl `  r )
1613, 11, 15crab 2758 . . . 4  class  { j  e.  ( Idl `  r
)  |  s  C_  j }
1716cint 4227 . . 3  class  |^| { j  e.  ( Idl `  r
)  |  s  C_  j }
182, 3, 4, 9, 17cmpt2 6280 . 2  class  ( r  e.  RingOps ,  s  e. 
~P ran  ( 1st `  r )  |->  |^| { j  e.  ( Idl `  r
)  |  s  C_  j } )
191, 18wceq 1405 1  wff  IdlGen  =  ( r  e.  RingOps ,  s  e.  ~P ran  ( 1st `  r )  |->  |^|
{ j  e.  ( Idl `  r )  |  s  C_  j } )
Colors of variables: wff setvar class
This definition is referenced by:  igenval  31740
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