Definition df-zrng 33610

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 33601	. 2 class ZRing
2		vr	. . 3 setvar 𝑟
3		cvv 3431	. . 3 class V
4	2	cv 1541	. . . 4 class 𝑟
5		czrh 20699	. . . . . 6 class ℤRHom
6	4, 5	cfv 6432	. . . . 5 class (ℤRHom‘𝑟)
7	6	crn 5591	. . . 4 class ran (ℤRHom‘𝑟)
8		citr 33585	. . . 4 class IntgRing
9	4, 7, 8	co 7271	. . 3 class (𝑟 IntgRing ran (ℤRHom‘𝑟))
10	2, 3, 9	cmpt 5162	. 2 class (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))
11	1, 10	wceq 1542	1 wff ZRing = (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))

This definition is referenced by: (None)