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

Definition df-invr 15736
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 15735 . 2  class  invr
2 vr . . 3  set  r
3 cvv 2920 . . 3  class  _V
42cv 1648 . . . . . 6  class  r
5 cmgp 15607 . . . . . 6  class mulGrp
64, 5cfv 5417 . . . . 5  class  (mulGrp `  r )
7 cui 15703 . . . . . 6  class Unit
84, 7cfv 5417 . . . . 5  class  (Unit `  r )
9 cress 13429 . . . . 5  classs
106, 8, 9co 6044 . . . 4  class  ( (mulGrp `  r )s  (Unit `  r )
)
11 cminusg 14645 . . . 4  class  inv g
1210, 11cfv 5417 . . 3  class  ( inv g `  ( (mulGrp `  r )s  (Unit `  r )
) )
132, 3, 12cmpt 4230 . 2  class  ( r  e.  _V  |->  ( inv g `  ( (mulGrp `  r )s  (Unit `  r )
) ) )
141, 13wceq 1649 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  15737
  Copyright terms: Public domain W3C validator