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Definition df-csgrp2 41640
Description: A commutative semigroup is a semigroup with a commutative operation. (Contributed by AV, 20-Jan-2020.)
Assertion
Ref Expression
df-csgrp2 CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g𝑔) comLaw (Base‘𝑔)}

Detailed syntax breakdown of Definition df-csgrp2
StepHypRef Expression
1 ccsgrp2 41636 . 2 class CSGrpALT
2 vg . . . . . 6 setvar 𝑔
32cv 1474 . . . . 5 class 𝑔
4 cplusg 15717 . . . . 5 class +g
53, 4cfv 5790 . . . 4 class (+g𝑔)
6 cbs 15644 . . . . 5 class Base
73, 6cfv 5790 . . . 4 class (Base‘𝑔)
8 ccomlaw 41603 . . . 4 class comLaw
95, 7, 8wbr 4578 . . 3 wff (+g𝑔) comLaw (Base‘𝑔)
10 csgrp2 41635 . . 3 class SGrpALT
119, 2, 10crab 2900 . 2 class {𝑔 ∈ SGrpALT ∣ (+g𝑔) comLaw (Base‘𝑔)}
121, 11wceq 1475 1 wff CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g𝑔) comLaw (Base‘𝑔)}
Colors of variables: wff setvar class
This definition is referenced by:  iscsgrpALT  41644
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