Definition df-zrng 35645

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

Assertion

Ref	Expression
df-zrng	⊢ ZRing = (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))

Detailed syntax breakdown of Definition df-zrng

Step	Hyp	Ref	Expression
1		czr 35636	. 2 class ZRing
2		vr	. . 3 setvar 𝑟
3		cvv 3455	. . 3 class V
4	2	cv 1539	. . . 4 class 𝑟
5		czrh 21415	. . . . . 6 class ℤRHom
6	4, 5	cfv 6519	. . . . 5 class (ℤRHom‘𝑟)
7	6	crn 5647	. . . 4 class ran (ℤRHom‘𝑟)
8		cirng 33686	. . . 4 class IntgRing
9	4, 7, 8	co 7394	. . 3 class (𝑟 IntgRing ran (ℤRHom‘𝑟))
10	2, 3, 9	cmpt 5196	. 2 class (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))
11	1, 10	wceq 1540	1 wff ZRing = (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))

This definition is referenced by: (None)