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Definition df-lpir 15996
Description: Define the class of left principal ideal rings, rings where every left ideal has a single generator. (Contributed by Stefan O'Rear, 3-Jan-2015.)
Assertion
Ref Expression
df-lpir  |- LPIR  =  {
w  e.  Ring  |  (LIdeal `  w )  =  (LPIdeal `  w ) }

Detailed syntax breakdown of Definition df-lpir
StepHypRef Expression
1 clpir 15994 . 2  class LPIR
2 vw . . . . . 6  set  w
32cv 1622 . . . . 5  class  w
4 clidl 15923 . . . . 5  class LIdeal
53, 4cfv 5255 . . . 4  class  (LIdeal `  w )
6 clpidl 15993 . . . . 5  class LPIdeal
73, 6cfv 5255 . . . 4  class  (LPIdeal `  w
)
85, 7wceq 1623 . . 3  wff  (LIdeal `  w )  =  (LPIdeal `  w )
9 crg 15337 . . 3  class  Ring
108, 2, 9crab 2547 . 2  class  { w  e.  Ring  |  (LIdeal `  w )  =  (LPIdeal `  w ) }
111, 10wceq 1623 1  wff LPIR  =  {
w  e.  Ring  |  (LIdeal `  w )  =  (LPIdeal `  w ) }
Colors of variables: wff set class
This definition is referenced by:  islpir  16001
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