Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-csgrp2 Structured version   Visualization version   GIF version

Definition df-csgrp2 44412
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 44408 . 2 class CSGrpALT
2 vg . . . . . 6 setvar 𝑔
32cv 1537 . . . . 5 class 𝑔
4 cplusg 16565 . . . . 5 class +g
53, 4cfv 6343 . . . 4 class (+g𝑔)
6 cbs 16483 . . . . 5 class Base
73, 6cfv 6343 . . . 4 class (Base‘𝑔)
8 ccomlaw 44375 . . . 4 class comLaw
95, 7, 8wbr 5052 . . 3 wff (+g𝑔) comLaw (Base‘𝑔)
10 csgrp2 44407 . . 3 class SGrpALT
119, 2, 10crab 3137 . 2 class {𝑔 ∈ SGrpALT ∣ (+g𝑔) comLaw (Base‘𝑔)}
121, 11wceq 1538 1 wff CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g𝑔) comLaw (Base‘𝑔)}
Colors of variables: wff setvar class
This definition is referenced by:  iscsgrpALT  44416
  Copyright terms: Public domain W3C validator