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Definition df-zrh 20046
Description: Define the unique homomorphism from the integers into a ring. This encodes the usual notation of 𝑛 = 1r + 1r + ... + 1r for integers (see also df-mulg 17734). (Contributed by Mario Carneiro, 13-Jun-2015.) (Revised by AV, 12-Jun-2019.)
Assertion
Ref Expression
df-zrh ℤRHom = (𝑟 ∈ V ↦ (ℤring RingHom 𝑟))

Detailed syntax breakdown of Definition df-zrh
StepHypRef Expression
1 czrh 20042 . 2 class ℤRHom
2 vr . . 3 setvar 𝑟
3 cvv 3332 . . 3 class V
4 zring 20012 . . . . 5 class ring
52cv 1623 . . . . 5 class 𝑟
6 crh 18906 . . . . 5 class RingHom
74, 5, 6co 6805 . . . 4 class (ℤring RingHom 𝑟)
87cuni 4580 . . 3 class (ℤring RingHom 𝑟)
92, 3, 8cmpt 4873 . 2 class (𝑟 ∈ V ↦ (ℤring RingHom 𝑟))
101, 9wceq 1624 1 wff ℤRHom = (𝑟 ∈ V ↦ (ℤring RingHom 𝑟))
Colors of variables: wff setvar class
This definition is referenced by:  zrhval  20050
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