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

Definition df-cntr 18443
 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 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚)))

Detailed syntax breakdown of Definition df-cntr
StepHypRef Expression
1 ccntr 18441 . 2 class Cntr
2 vm . . 3 setvar 𝑚
3 cvv 3444 . . 3 class V
42cv 1537 . . . . 5 class 𝑚
5 cbs 16478 . . . . 5 class Base
64, 5cfv 6328 . . . 4 class (Base‘𝑚)
7 ccntz 18440 . . . . 5 class Cntz
84, 7cfv 6328 . . . 4 class (Cntz‘𝑚)
96, 8cfv 6328 . . 3 class ((Cntz‘𝑚)‘(Base‘𝑚))
102, 3, 9cmpt 5113 . 2 class (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚)))
111, 10wceq 1538 1 wff Cntr = (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚)))
 Colors of variables: wff setvar class This definition is referenced by:  cntrval  18444
 Copyright terms: Public domain W3C validator