Definition df-csring 41154

Description: Define the class of all commutative semirings. (Contributed by metakunt, 4-Apr-2025.)

Assertion

Ref	Expression
df-csring	⊢ CSRing = {𝑓 ∈ SRing ∣ (mulGrp‘𝑓) ∈ CMnd}

Detailed syntax breakdown of Definition df-csring

Step	Hyp	Ref	Expression
1		ccsrg 41153	. 2 class CSRing
2		vf	. . . . . 6 setvar 𝑓
3	2	cv 1539	. . . . 5 class 𝑓
4		cmgp 20032	. . . . 5 class mulGrp
5	3, 4	cfv 6543	. . . 4 class (mulGrp‘𝑓)
6		ccmn 19693	. . . 4 class CMnd
7	5, 6	wcel 2105	. . 3 wff (mulGrp‘𝑓) ∈ CMnd
8		csrg 20084	. . 3 class SRing
9	7, 2, 8	crab 3431	. 2 class {𝑓 ∈ SRing ∣ (mulGrp‘𝑓) ∈ CMnd}
10	1, 9	wceq 1540	1 wff CSRing = {𝑓 ∈ SRing ∣ (mulGrp‘𝑓) ∈ CMnd}

This definition is referenced by:  iscsrg  41155