Definition df-cring 13180

Description: Define class of all commutative rings. (Contributed by Mario Carneiro, 7-Jan-2015.)

Assertion

Ref	Expression
df-cring	|- CRing = { f e. Ring | (mulGrp ` f ) e. CMnd }

Detailed syntax breakdown of Definition df-cring

Step	Hyp	Ref	Expression
1		ccrg 13178	. 2 class CRing
2		vf	. . . . . 6 setvar f
3	2	cv 1352	. . . . 5 class f
4		cmgp 13128	. . . . 5 class mulGrp
5	3, 4	cfv 5216	. . . 4 class (mulGrp ` f )
6		ccmn 13086	. . . 4 class CMnd
7	5, 6	wcel 2148	. . 3 wff (mulGrp ` f ) e. CMnd
8		crg 13177	. . 3 class Ring
9	7, 2, 8	crab 2459	. 2 class { f e. Ring | (mulGrp ` f ) e. CMnd }
10	1, 9	wceq 1353	1 wff CRing = { f e. Ring | (mulGrp ` f ) e. CMnd }

This definition is referenced by:  iscrng  13184