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Definition df-zrh 17910
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 15539). (Contributed by Mario Carneiro, 13-Jun-2015.) (Revised by AV, 12-Jun-2019.)
Assertion
Ref Expression
df-zrh  |-  ZRHom  =  ( r  e.  _V  |->  U. (ring RingHom  r ) )

Detailed syntax breakdown of Definition df-zrh
StepHypRef Expression
1 czrh 17906 . 2  class  ZRHom
2 vr . . 3  setvar  r
3 cvv 2967 . . 3  class  _V
4 zring 17858 . . . . 5  classring
52cv 1368 . . . . 5  class  r
6 crh 16792 . . . . 5  class RingHom
74, 5, 6co 6086 . . . 4  class  (ring RingHom  r )
87cuni 4086 . . 3  class  U. (ring RingHom  r )
92, 3, 8cmpt 4345 . 2  class  ( r  e.  _V  |->  U. (ring RingHom  r ) )
101, 9wceq 1369 1  wff  ZRHom  =  ( r  e.  _V  |->  U. (ring RingHom  r ) )
Colors of variables: wff setvar class
This definition is referenced by:  zrhval  17914
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