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

Definition df-oppr 15405
Description: Define an opposite ring, which is the same as the original ring but with multiplication written the other way around. (Contributed by Mario Carneiro, 1-Dec-2014.)
Assertion
Ref Expression
df-oppr  |- oppr  =  ( f  e.  _V  |->  ( f sSet  <. ( .r `  ndx ) , tpos  ( .r `  f
) >. ) )

Detailed syntax breakdown of Definition df-oppr
StepHypRef Expression
1 coppr 15404 . 2  class oppr
2 vf . . 3  set  f
3 cvv 2788 . . 3  class  _V
42cv 1622 . . . 4  class  f
5 cnx 13145 . . . . . 6  class  ndx
6 cmulr 13209 . . . . . 6  class  .r
75, 6cfv 5255 . . . . 5  class  ( .r
`  ndx )
84, 6cfv 5255 . . . . . 6  class  ( .r
`  f )
98ctpos 6233 . . . . 5  class tpos  ( .r
`  f )
107, 9cop 3643 . . . 4  class  <. ( .r `  ndx ) , tpos  ( .r `  f
) >.
11 csts 13146 . . . 4  class sSet
124, 10, 11co 5858 . . 3  class  ( f sSet  <. ( .r `  ndx ) , tpos  ( .r `  f ) >. )
132, 3, 12cmpt 4077 . 2  class  ( f  e.  _V  |->  ( f sSet  <. ( .r `  ndx ) , tpos  ( .r `  f ) >. )
)
141, 13wceq 1623 1  wff oppr  =  ( f  e.  _V  |->  ( f sSet  <. ( .r `  ndx ) , tpos  ( .r `  f
) >. ) )
Colors of variables: wff set class
This definition is referenced by:  opprval  15406
  Copyright terms: Public domain W3C validator