MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-2idl Unicode version

Definition df-2idl 16000
Description: Define the class of two-sided ideals of a ring. A two-sided ideal is a left ideal which is also a right ideal (or a left ideal over the opposite ring). (Contributed by Mario Carneiro, 14-Jun-2015.)
Assertion
Ref Expression
df-2idl  |- 2Ideal  =  ( r  e.  _V  |->  ( (LIdeal `  r )  i^i  (LIdeal `  (oppr
`  r ) ) ) )

Detailed syntax breakdown of Definition df-2idl
StepHypRef Expression
1 c2idl 15999 . 2  class 2Ideal
2 vr . . 3  set  r
3 cvv 2801 . . 3  class  _V
42cv 1631 . . . . 5  class  r
5 clidl 15939 . . . . 5  class LIdeal
64, 5cfv 5271 . . . 4  class  (LIdeal `  r )
7 coppr 15420 . . . . . 6  class oppr
84, 7cfv 5271 . . . . 5  class  (oppr `  r
)
98, 5cfv 5271 . . . 4  class  (LIdeal `  (oppr `  r ) )
106, 9cin 3164 . . 3  class  ( (LIdeal `  r )  i^i  (LIdeal `  (oppr
`  r ) ) )
112, 3, 10cmpt 4093 . 2  class  ( r  e.  _V  |->  ( (LIdeal `  r )  i^i  (LIdeal `  (oppr
`  r ) ) ) )
121, 11wceq 1632 1  wff 2Ideal  =  ( r  e.  _V  |->  ( (LIdeal `  r )  i^i  (LIdeal `  (oppr
`  r ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  2idlval  16001
  Copyright terms: Public domain W3C validator