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Definition df-invr 15454
Description: Define multiplicative inverse. (Contributed by NM, 21-Sep-2011.)
Assertion
Ref Expression
df-invr  |-  invr  =  ( r  e.  _V  |->  ( inv g `  (
(mulGrp `  r )s  (Unit `  r ) ) ) )

Detailed syntax breakdown of Definition df-invr
StepHypRef Expression
1 cinvr 15453 . 2  class  invr
2 vr . . 3  set  r
3 cvv 2788 . . 3  class  _V
42cv 1622 . . . . . 6  class  r
5 cmgp 15325 . . . . . 6  class mulGrp
64, 5cfv 5255 . . . . 5  class  (mulGrp `  r )
7 cui 15421 . . . . . 6  class Unit
84, 7cfv 5255 . . . . 5  class  (Unit `  r )
9 cress 13149 . . . . 5  classs
106, 8, 9co 5858 . . . 4  class  ( (mulGrp `  r )s  (Unit `  r )
)
11 cminusg 14363 . . . 4  class  inv g
1210, 11cfv 5255 . . 3  class  ( inv g `  ( (mulGrp `  r )s  (Unit `  r )
) )
132, 3, 12cmpt 4077 . 2  class  ( r  e.  _V  |->  ( inv g `  ( (mulGrp `  r )s  (Unit `  r )
) ) )
141, 13wceq 1623 1  wff  invr  =  ( r  e.  _V  |->  ( inv g `  (
(mulGrp `  r )s  (Unit `  r ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  invrfval  15455
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