Definition df-chr 19854

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 e. _V |-> ( ( od ` g ) ` ( 1r ` g ) ) )

Detailed syntax breakdown of Definition df-chr

Step	Hyp	Ref	Expression
1		cchr 19850	. 2 class chr
2		vg	. . 3 setvar g
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . . 5 class g
5		cur 18501	. . . . 5 class 1r
6	4, 5	cfv 5888	. . . 4 class ( 1r ` g )
7		cod 17944	. . . . 5 class od
8	4, 7	cfv 5888	. . . 4 class ( od ` g )
9	6, 8	cfv 5888	. . 3 class ( ( od ` g ) ` ( 1r ` g ) )
10	2, 3, 9	cmpt 4729	. 2 class ( g e. _V |-> ( ( od ` g ) ` ( 1r ` g ) ) )
11	1, 10	wceq 1483	1 wff chr = ( g e. _V |-> ( ( od ` g ) ` ( 1r ` g ) ) )

This definition is referenced by:  chrval  19873