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Definition df-invr 16700
Description: Define multiplicative inverse. (Contributed by NM, 21-Sep-2011.)
Assertion
Ref Expression
df-invr  |-  invr  =  ( r  e.  _V  |->  ( invg `  (
(mulGrp `  r )s  (Unit `  r ) ) ) )

Detailed syntax breakdown of Definition df-invr
StepHypRef Expression
1 cinvr 16699 . 2  class  invr
2 vr . . 3  setvar  r
3 cvv 2964 . . 3  class  _V
42cv 1363 . . . . . 6  class  r
5 cmgp 16567 . . . . . 6  class mulGrp
64, 5cfv 5408 . . . . 5  class  (mulGrp `  r )
7 cui 16667 . . . . . 6  class Unit
84, 7cfv 5408 . . . . 5  class  (Unit `  r )
9 cress 14160 . . . . 5  classs
106, 8, 9co 6082 . . . 4  class  ( (mulGrp `  r )s  (Unit `  r )
)
11 cminusg 15396 . . . 4  class  invg
1210, 11cfv 5408 . . 3  class  ( invg `  ( (mulGrp `  r )s  (Unit `  r )
) )
132, 3, 12cmpt 4340 . 2  class  ( r  e.  _V  |->  ( invg `  ( (mulGrp `  r )s  (Unit `  r )
) ) )
141, 13wceq 1364 1  wff  invr  =  ( r  e.  _V  |->  ( invg `  (
(mulGrp `  r )s  (Unit `  r ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  invrfval  16701
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