Definition df-sgrp2 41857

Description: A semigroup is a magma with an associative operation. Definition in section II.1 of [Bruck] p. 23, or of an "associative magma" in definition 5 of [BourbakiAlg1] p. 4, or of a semi-group in section 1.3 of [Hall] p. 7. (Contributed by AV, 6-Jan-2020.)

Assertion

Ref	Expression
df-sgrp2	|- SGrpALT = { g e. MgmALT | ( +g ` g ) assLaw ( Base ` g ) }

Detailed syntax breakdown of Definition df-sgrp2

Step	Hyp	Ref	Expression
1		csgrp2 41853	. 2 class SGrpALT
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		casslaw 41820	. . . 4 class assLaw
9	5, 7, 8	wbr 4653	. . 3 wff ( +g ` g ) assLaw ( Base ` g )
10		cmgm2 41851	. . 3 class MgmALT
11	9, 2, 10	crab 2916	. 2 class { g e. MgmALT | ( +g ` g ) assLaw ( Base ` g ) }
12	1, 11	wceq 1483	1 wff SGrpALT = { g e. MgmALT | ( +g ` g ) assLaw ( Base ` g ) }

This definition is referenced by:  issgrpALT  41861