Definition df-mgm2 41855

Description: A magma is a set equipped with a closed operation. Definition 1 of [BourbakiAlg1] p. 1, or definition of a groupoid in section I.1 of [Bruck] p. 1. Note: The term "groupoid" is now widely used to refer to other objects: (small) categories all of whose morphisms are invertible, or groups with a partial function replacing the binary operation. Therefore, we will only use the term "magma" for the present notion in set.mm. (Contributed by AV, 6-Jan-2020.)

Assertion

Ref	Expression
df-mgm2	|- MgmALT = { m | ( +g ` m ) clLaw ( Base ` m ) }

Detailed syntax breakdown of Definition df-mgm2

Step	Hyp	Ref	Expression
1		cmgm2 41851	. 2 class MgmALT
2		vm	. . . . . 6 setvar m
3	2	cv 1482	. . . . 5 class m
4		cplusg 15941	. . . . 5 class +g
5	3, 4	cfv 5888	. . . 4 class ( +g ` m )
6		cbs 15857	. . . . 5 class Base
7	3, 6	cfv 5888	. . . 4 class ( Base ` m )
8		ccllaw 41819	. . . 4 class clLaw
9	5, 7, 8	wbr 4653	. . 3 wff ( +g ` m ) clLaw ( Base ` m )
10	9, 2	cab 2608	. 2 class { m | ( +g ` m ) clLaw ( Base ` m ) }
11	1, 10	wceq 1483	1 wff MgmALT = { m | ( +g ` m ) clLaw ( Base ` m ) }

This definition is referenced by:  ismgmALT  41859