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Mirrors > Home > MPE Home > Th. List > df-cntr | Structured version Visualization version GIF version |
Description: Define the center of a magma, which is the elements that commute with all others. (Contributed by Stefan O'Rear, 5-Sep-2015.) |
Ref | Expression |
---|---|
df-cntr | ⊢ Cntr = (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccntr 18920 | . 2 class Cntr | |
2 | vm | . . 3 setvar 𝑚 | |
3 | cvv 3431 | . . 3 class V | |
4 | 2 | cv 1541 | . . . . 5 class 𝑚 |
5 | cbs 16910 | . . . . 5 class Base | |
6 | 4, 5 | cfv 6432 | . . . 4 class (Base‘𝑚) |
7 | ccntz 18919 | . . . . 5 class Cntz | |
8 | 4, 7 | cfv 6432 | . . . 4 class (Cntz‘𝑚) |
9 | 6, 8 | cfv 6432 | . . 3 class ((Cntz‘𝑚)‘(Base‘𝑚)) |
10 | 2, 3, 9 | cmpt 5162 | . 2 class (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚))) |
11 | 1, 10 | wceq 1542 | 1 wff Cntr = (𝑚 ∈ V ↦ ((Cntz‘𝑚)‘(Base‘𝑚))) |
Colors of variables: wff setvar class |
This definition is referenced by: cntrval 18923 |
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