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

Definition df-chr 20069
Description: The characteristic of a ring is the smallest positive integer which is equal to 0 when interpreted in the ring, or 0 if there is no such positive integer. (Contributed by Stefan O'Rear, 5-Sep-2015.)
Assertion
Ref Expression
df-chr chr = (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r𝑔)))

Detailed syntax breakdown of Definition df-chr
StepHypRef Expression
1 cchr 20065 . 2 class chr
2 vg . . 3 setvar 𝑔
3 cvv 3351 . . 3 class V
42cv 1630 . . . . 5 class 𝑔
5 cur 18709 . . . . 5 class 1r
64, 5cfv 6031 . . . 4 class (1r𝑔)
7 cod 18151 . . . . 5 class od
84, 7cfv 6031 . . . 4 class (od‘𝑔)
96, 8cfv 6031 . . 3 class ((od‘𝑔)‘(1r𝑔))
102, 3, 9cmpt 4863 . 2 class (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r𝑔)))
111, 10wceq 1631 1 wff chr = (𝑔 ∈ V ↦ ((od‘𝑔)‘(1r𝑔)))
Colors of variables: wff setvar class
This definition is referenced by:  chrval  20088
  Copyright terms: Public domain W3C validator