Definition df-csgrp2 41858

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

Assertion

Ref	Expression
df-csgrp2	|- CSGrpALT = { g e. SGrpALT | ( +g ` g ) comLaw ( Base ` g ) }

Detailed syntax breakdown of Definition df-csgrp2

Step	Hyp	Ref	Expression
1		ccsgrp2 41854	. 2 class CSGrpALT
2		vg	. . . . . 6 setvar g
3	2	cv 1482	. . . . 5 class g
4		cplusg 15941	. . . . 5 class +g
5	3, 4	cfv 5888	. . . 4 class ( +g ` g )
6		cbs 15857	. . . . 5 class Base
7	3, 6	cfv 5888	. . . 4 class ( Base ` g )
8		ccomlaw 41821	. . . 4 class comLaw
9	5, 7, 8	wbr 4653	. . 3 wff ( +g ` g ) comLaw ( Base ` g )
10		csgrp2 41853	. . 3 class SGrpALT
11	9, 2, 10	crab 2916	. 2 class { g e. SGrpALT | ( +g ` g ) comLaw ( Base ` g ) }
12	1, 11	wceq 1483	1 wff CSGrpALT = { g e. SGrpALT | ( +g ` g ) comLaw ( Base ` g ) }

This definition is referenced by:  iscsgrpALT  41862