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Definition df-ur 15342
Description: Define the multiplicative neutral element of a ring. This definition works by extracting the  0g element, i.e. the neutral element in a group or monoid, and transfering it to the multiplicative monoid via the mulGrp function (df-mgp 15326). See also dfur2 15344, which derives the "traditional" definition as the unique element of a ring which is left- and right-neutral under multiplication. (Contributed by NM, 27-Aug-2011.) (Revised by Mario Carneiro, 27-Dec-2014.)
Assertion
Ref Expression
df-ur  |-  1r  =  ( 0g  o. mulGrp )

Detailed syntax breakdown of Definition df-ur
StepHypRef Expression
1 cur 15339 . 2  class  1r
2 c0g 13400 . . 3  class  0g
3 cmgp 15325 . . 3  class mulGrp
42, 3ccom 4693 . 2  class  ( 0g  o. mulGrp )
51, 4wceq 1623 1  wff  1r  =  ( 0g  o. mulGrp )
Colors of variables: wff set class
This definition is referenced by:  rngidval  15343  prds1  15397  pws1  15399
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