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

Step	Hyp	Ref	Expression
1		cur 15339	. 2 class 1r
2		c0g 13400	. . 3 class 0g
3		cmgp 15325	. . 3 class mulGrp
4	2, 3	ccom 4693	. 2 class ( 0g o. mulGrp )
5	1, 4	wceq 1623	1 wff 1r = ( 0g o. mulGrp )

This definition is referenced by:  rngidval  15343  prds1  15397  pws1  15399