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Definition df-ur 18707
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 18695). See also dfur2 18709, 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 ∘ mulGrp)

Detailed syntax breakdown of Definition df-ur
StepHypRef Expression
1 cur 18706 . 2 class 1r
2 c0g 16308 . . 3 class 0g
3 cmgp 18694 . . 3 class mulGrp
42, 3ccom 5322 . 2 class (0g ∘ mulGrp)
51, 4wceq 1637 1 wff 1r = (0g ∘ mulGrp)
Colors of variables: wff setvar class
This definition is referenced by:  ringidval  18708  prds1  18819  pws1  18821
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