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Definition df-zrng 30595
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
StepHypRef Expression
1 czr 30585 . 2 class ZRing
2 vr . . 3 setvar 𝑟
3 cvv 3172 . . 3 class V
42cv 1473 . . . 4 class 𝑟
5 czrh 19614 . . . . . 6 class ℤRHom
64, 5cfv 5789 . . . . 5 class (ℤRHom‘𝑟)
76crn 5028 . . . 4 class ran (ℤRHom‘𝑟)
8 citr 30569 . . . 4 class IntgRing
94, 7, 8co 6526 . . 3 class (𝑟 IntgRing ran (ℤRHom‘𝑟))
102, 3, 9cmpt 4637 . 2 class (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))
111, 10wceq 1474 1 wff ZRing = (𝑟 ∈ V ↦ (𝑟 IntgRing ran (ℤRHom‘𝑟)))
Colors of variables: wff setvar class
This definition is referenced by: (None)
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