Definition df-csgrp2 41648

Description: A commutative semigroup is a semigroup with a commutative operation. (Contributed by AV, 20-Jan-2020.)

Assertion

Ref	Expression
df-csgrp2	⊢ CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g‘𝑔) comLaw (Base‘𝑔)}

Detailed syntax breakdown of Definition df-csgrp2

Step	Hyp	Ref	Expression
1		ccsgrp2 41644	. 2 class CSGrpALT
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1474	. . . . 5 class 𝑔
4		cplusg 15768	. . . . 5 class +g
5	3, 4	cfv 5804	. . . 4 class (+g‘𝑔)
6		cbs 15695	. . . . 5 class Base
7	3, 6	cfv 5804	. . . 4 class (Base‘𝑔)
8		ccomlaw 41611	. . . 4 class comLaw
9	5, 7, 8	wbr 4583	. . 3 wff (+g‘𝑔) comLaw (Base‘𝑔)
10		csgrp2 41643	. . 3 class SGrpALT
11	9, 2, 10	crab 2900	. 2 class {𝑔 ∈ SGrpALT ∣ (+g‘𝑔) comLaw (Base‘𝑔)}
12	1, 11	wceq 1475	1 wff CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g‘𝑔) comLaw (Base‘𝑔)}

This definition is referenced by:  iscsgrpALT  41652