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Definition df-mgm2 42654
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 ∣ (+g𝑚) clLaw (Base‘𝑚)}

Detailed syntax breakdown of Definition df-mgm2
StepHypRef Expression
1 cmgm2 42650 . 2 class MgmALT
2 vm . . . . . 6 setvar 𝑚
32cv 1652 . . . . 5 class 𝑚
4 cplusg 16267 . . . . 5 class +g
53, 4cfv 6101 . . . 4 class (+g𝑚)
6 cbs 16184 . . . . 5 class Base
73, 6cfv 6101 . . . 4 class (Base‘𝑚)
8 ccllaw 42618 . . . 4 class clLaw
95, 7, 8wbr 4843 . . 3 wff (+g𝑚) clLaw (Base‘𝑚)
109, 2cab 2785 . 2 class {𝑚 ∣ (+g𝑚) clLaw (Base‘𝑚)}
111, 10wceq 1653 1 wff MgmALT = {𝑚 ∣ (+g𝑚) clLaw (Base‘𝑚)}
Colors of variables: wff setvar class
This definition is referenced by:  ismgmALT  42658
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