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Definition df-cring 17180
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
StepHypRef Expression
1 ccrg 17178 . 2  class  CRing
2 vf . . . . . 6  setvar  f
32cv 1382 . . . . 5  class  f
4 cmgp 17120 . . . . 5  class mulGrp
53, 4cfv 5578 . . . 4  class  (mulGrp `  f )
6 ccmn 16777 . . . 4  class CMnd
75, 6wcel 1804 . . 3  wff  (mulGrp `  f )  e. CMnd
8 crg 17177 . . 3  class  Ring
97, 2, 8crab 2797 . 2  class  { f  e.  Ring  |  (mulGrp `  f )  e. CMnd }
101, 9wceq 1383 1  wff  CRing  =  {
f  e.  Ring  |  (mulGrp `  f )  e. CMnd }
Colors of variables: wff setvar class
This definition is referenced by:  iscrng  17184
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