Definition df-zrng 31548

Description: Define the subring of integral elements in a ring. (Contributed by Mario Carneiro, 2-Dec-2014.)

Assertion

Ref	Expression
df-zrng	|- ZRing = ( r e. _V |-> ( r IntgRing ran ( ZRHom ` r ) ) )

Detailed syntax breakdown of Definition df-zrng

Step	Hyp	Ref	Expression
1		czr 31538	. 2 class ZRing
2		vr	. . 3 setvar r
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . 4 class r
5		czrh 19848	. . . . . 6 class ZRHom
6	4, 5	cfv 5888	. . . . 5 class ( ZRHom ` r )
7	6	crn 5115	. . . 4 class ran ( ZRHom ` r )
8		citr 31522	. . . 4 class IntgRing
9	4, 7, 8	co 6650	. . 3 class ( r IntgRing ran ( ZRHom ` r ) )
10	2, 3, 9	cmpt 4729	. 2 class ( r e. _V |-> ( r IntgRing ran ( ZRHom ` r ) ) )
11	1, 10	wceq 1483	1 wff ZRing = ( r e. _V |-> ( r IntgRing ran ( ZRHom ` r ) ) )

This definition is referenced by: (None)