Definition df-cmgm2 45414

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 ∣ (+g‘𝑚) comLaw (Base‘𝑚)}

Detailed syntax breakdown of Definition df-cmgm2

Step	Hyp	Ref	Expression
1		ccmgm2 45410	. 2 class CMgmALT
2		vm	. . . . . 6 setvar 𝑚
3	2	cv 1538	. . . . 5 class 𝑚
4		cplusg 16962	. . . . 5 class +g
5	3, 4	cfv 6433	. . . 4 class (+g‘𝑚)
6		cbs 16912	. . . . 5 class Base
7	3, 6	cfv 6433	. . . 4 class (Base‘𝑚)
8		ccomlaw 45379	. . . 4 class comLaw
9	5, 7, 8	wbr 5074	. . 3 wff (+g‘𝑚) comLaw (Base‘𝑚)
10		cmgm2 45409	. . 3 class MgmALT
11	9, 2, 10	crab 3068	. 2 class {𝑚 ∈ MgmALT ∣ (+g‘𝑚) comLaw (Base‘𝑚)}
12	1, 11	wceq 1539	1 wff CMgmALT = {𝑚 ∈ MgmALT ∣ (+g‘𝑚) comLaw (Base‘𝑚)}

This definition is referenced by:  iscmgmALT  45418