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Definition df-rgmod 15942
Description: Every ring can be viewed as a left module over itself. (Contributed by Stefan O'Rear, 6-Dec-2014.)
Assertion
Ref Expression
df-rgmod  |- ringLMod  =  ( w  e.  _V  |->  ( ( subringAlg  `  w ) `  ( Base `  w )
) )

Detailed syntax breakdown of Definition df-rgmod
StepHypRef Expression
1 crglmod 15938 . 2  class ringLMod
2 vw . . 3  set  w
3 cvv 2801 . . 3  class  _V
42cv 1631 . . . . 5  class  w
5 cbs 13164 . . . . 5  class  Base
64, 5cfv 5271 . . . 4  class  ( Base `  w )
7 csra 15937 . . . . 5  class subringAlg
84, 7cfv 5271 . . . 4  class  ( subringAlg  `  w
)
96, 8cfv 5271 . . 3  class  ( ( subringAlg  `  w ) `  ( Base `  w ) )
102, 3, 9cmpt 4093 . 2  class  ( w  e.  _V  |->  ( ( subringAlg  `  w ) `  ( Base `  w ) ) )
111, 10wceq 1632 1  wff ringLMod  =  ( w  e.  _V  |->  ( ( subringAlg  `  w ) `  ( Base `  w )
) )
Colors of variables: wff set class
This definition is referenced by:  rlmfn  15960  rlmval  15961
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