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

Definition df-cntr 15841
Description: Define the center of a magma, which is the elements that commute with all others. (Contributed by Stefan O'Rear, 5-Sep-2015.)
Assertion
Ref Expression
df-cntr  |- Cntr  =  ( m  e.  _V  |->  ( (Cntz `  m ) `  ( Base `  m
) ) )

Detailed syntax breakdown of Definition df-cntr
StepHypRef Expression
1 ccntr 15839 . 2  class Cntr
2 vm . . 3  setvar  m
3 cvv 2977 . . 3  class  _V
42cv 1368 . . . . 5  class  m
5 cbs 14179 . . . . 5  class  Base
64, 5cfv 5423 . . . 4  class  ( Base `  m )
7 ccntz 15838 . . . . 5  class Cntz
84, 7cfv 5423 . . . 4  class  (Cntz `  m )
96, 8cfv 5423 . . 3  class  ( (Cntz `  m ) `  ( Base `  m ) )
102, 3, 9cmpt 4355 . 2  class  ( m  e.  _V  |->  ( (Cntz `  m ) `  ( Base `  m ) ) )
111, 10wceq 1369 1  wff Cntr  =  ( m  e.  _V  |->  ( (Cntz `  m ) `  ( Base `  m
) ) )
Colors of variables: wff setvar class
This definition is referenced by:  cntrval  15842
  Copyright terms: Public domain W3C validator