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Definition df-cring 18748
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
StepHypRef Expression
1 ccrg 18746 . 2 class CRing
2 vf . . . . . 6 setvar 𝑓
32cv 1636 . . . . 5 class 𝑓
4 cmgp 18687 . . . . 5 class mulGrp
53, 4cfv 6097 . . . 4 class (mulGrp‘𝑓)
6 ccmn 18390 . . . 4 class CMnd
75, 6wcel 2156 . . 3 wff (mulGrp‘𝑓) ∈ CMnd
8 crg 18745 . . 3 class Ring
97, 2, 8crab 3100 . 2 class {𝑓 ∈ Ring ∣ (mulGrp‘𝑓) ∈ CMnd}
101, 9wceq 1637 1 wff CRing = {𝑓 ∈ Ring ∣ (mulGrp‘𝑓) ∈ CMnd}
Colors of variables: wff setvar class
This definition is referenced by:  iscrng  18752
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