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Definition df-ur 16582
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 transferring it to the multiplicative monoid via the mulGrp function (df-mgp 16566). See also dfur2 16584, 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 16579 . 2  class  1r
2 c0g 14361 . . 3  class  0g
3 cmgp 16565 . . 3  class mulGrp
42, 3ccom 4831 . 2  class  ( 0g  o. mulGrp )
51, 4wceq 1362 1  wff  1r  =  ( 0g  o. mulGrp )
Colors of variables: wff setvar class
This definition is referenced by:  rngidval  16583  prds1  16641  pws1  16643
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