Definition df-mgm2 44116

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 44112	. 2 class MgmALT
2		vm	. . . . . 6 setvar 𝑚
3	2	cv 1530	. . . . 5 class 𝑚
4		cplusg 16557	. . . . 5 class +g
5	3, 4	cfv 6348	. . . 4 class (+g‘𝑚)
6		cbs 16475	. . . . 5 class Base
7	3, 6	cfv 6348	. . . 4 class (Base‘𝑚)
8		ccllaw 44080	. . . 4 class clLaw
9	5, 7, 8	wbr 5057	. . 3 wff (+g‘𝑚) clLaw (Base‘𝑚)
10	9, 2	cab 2797	. 2 class {𝑚 ∣ (+g‘𝑚) clLaw (Base‘𝑚)}
11	1, 10	wceq 1531	1 wff MgmALT = {𝑚 ∣ (+g‘𝑚) clLaw (Base‘𝑚)}

This definition is referenced by:  ismgmALT  44120