Definition df-cring 20233

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

Assertion

Ref	Expression
df-cring	⊢ CRing = {𝑓 ∈ Ring ∣ (mulGrp‘𝑓) ∈ CMnd}

Detailed syntax breakdown of Definition df-cring

Step	Hyp	Ref	Expression
1		ccrg 20231	. 2 class CRing
2		vf	. . . . . 6 setvar 𝑓
3	2	cv 1539	. . . . 5 class 𝑓
4		cmgp 20137	. . . . 5 class mulGrp
5	3, 4	cfv 6561	. . . 4 class (mulGrp‘𝑓)
6		ccmn 19798	. . . 4 class CMnd
7	5, 6	wcel 2108	. . 3 wff (mulGrp‘𝑓) ∈ CMnd
8		crg 20230	. . 3 class Ring
9	7, 2, 8	crab 3436	. 2 class {𝑓 ∈ Ring ∣ (mulGrp‘𝑓) ∈ CMnd}
10	1, 9	wceq 1540	1 wff CRing = {𝑓 ∈ Ring ∣ (mulGrp‘𝑓) ∈ CMnd}

This definition is referenced by:  iscrng  20237