Definition df-cntr 14143

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

Step	Hyp	Ref	Expression
1		ccntr 14141	. 2 class Cntr
2		vm	. . 3 setvar 𝑚
3		cvv 2821	. . 3 class V
4	2	cv 1401	. . . . 5 class 𝑚
5		cbs 13404	. . . . 5 class Base
6	4, 5	cfv 5377	. . . 4 class (Base‘𝑚)
7		ccntz 14140	. . . . 5 class Cntz
8	4, 7	cfv 5377	. . . 4 class (Cntz‘𝑚)
9	6, 8	cfv 5377	. . 3 class ((Cntz‘𝑚)‘(Base‘𝑚))
10	2, 3, 9	cmpt 4192	. 2 class (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚)))
11	1, 10	wceq 1402	1 wff Cntr = (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚)))

This definition is used by:  cntrval  14145