Definition df-csgrp2

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

	Ref	Expression
Assertion	df-csgrp2	$$⊢\mathrm{CSGrpALT}=\left\{g\in \mathrm{SGrpALT}|{+}_g\mathrm{comLaw}{\mathrm{Base}}_g\right\}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		ccsgrp2	$$class\mathrm{CSGrpALT}$$
1		vg	$$setvarg$$
2		csgrp2	$$class\mathrm{SGrpALT}$$
3		cplusg	$$class{+}_{𝑔}$$
4	1	cv	$$setvarg$$
5	4 3	cfv	$$class{+}_g$$
6		ccomlaw	$$class\mathrm{comLaw}$$
7		cbs	$$class\mathrm{Base}$$
8	4 7	cfv	$$class{\mathrm{Base}}_g$$
9	5 8 6	wbr	$$wff{+}_g\mathrm{comLaw}{\mathrm{Base}}_g$$
10	9 1 2	crab	$$class\left\{g\in \mathrm{SGrpALT}|{+}_g\mathrm{comLaw}{\mathrm{Base}}_g\right\}$$
11	0 10	wceq	$$wff\mathrm{CSGrpALT}=\left\{g\in \mathrm{SGrpALT}|{+}_g\mathrm{comLaw}{\mathrm{Base}}_g\right\}$$