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Definition df-cmgm2 45087
Description: A commutative magma is a magma with a commutative operation. Definition 8 of [BourbakiAlg1] p. 7. (Contributed by AV, 20-Jan-2020.)
Assertion
Ref Expression
df-cmgm2 CMgmALT = {𝑚 ∈ MgmALT ∣ (+g𝑚) comLaw (Base‘𝑚)}

Detailed syntax breakdown of Definition df-cmgm2
StepHypRef Expression
1 ccmgm2 45083 . 2 class CMgmALT
2 vm . . . . . 6 setvar 𝑚
32cv 1542 . . . . 5 class 𝑚
4 cplusg 16802 . . . . 5 class +g
53, 4cfv 6380 . . . 4 class (+g𝑚)
6 cbs 16760 . . . . 5 class Base
73, 6cfv 6380 . . . 4 class (Base‘𝑚)
8 ccomlaw 45052 . . . 4 class comLaw
95, 7, 8wbr 5053 . . 3 wff (+g𝑚) comLaw (Base‘𝑚)
10 cmgm2 45082 . . 3 class MgmALT
119, 2, 10crab 3065 . 2 class {𝑚 ∈ MgmALT ∣ (+g𝑚) comLaw (Base‘𝑚)}
121, 11wceq 1543 1 wff CMgmALT = {𝑚 ∈ MgmALT ∣ (+g𝑚) comLaw (Base‘𝑚)}
Colors of variables: wff setvar class
This definition is referenced by:  iscmgmALT  45091
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