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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-csgrp2 | Structured version Visualization version GIF version |
Description: A commutative semigroup is a semigroup with a commutative operation. (Contributed by AV, 20-Jan-2020.) |
Ref | Expression |
---|---|
df-csgrp2 | ⊢ CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g‘𝑔) comLaw (Base‘𝑔)} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccsgrp2 41644 | . 2 class CSGrpALT | |
2 | vg | . . . . . 6 setvar 𝑔 | |
3 | 2 | cv 1474 | . . . . 5 class 𝑔 |
4 | cplusg 15768 | . . . . 5 class +g | |
5 | 3, 4 | cfv 5804 | . . . 4 class (+g‘𝑔) |
6 | cbs 15695 | . . . . 5 class Base | |
7 | 3, 6 | cfv 5804 | . . . 4 class (Base‘𝑔) |
8 | ccomlaw 41611 | . . . 4 class comLaw | |
9 | 5, 7, 8 | wbr 4583 | . . 3 wff (+g‘𝑔) comLaw (Base‘𝑔) |
10 | csgrp2 41643 | . . 3 class SGrpALT | |
11 | 9, 2, 10 | crab 2900 | . 2 class {𝑔 ∈ SGrpALT ∣ (+g‘𝑔) comLaw (Base‘𝑔)} |
12 | 1, 11 | wceq 1475 | 1 wff CSGrpALT = {𝑔 ∈ SGrpALT ∣ (+g‘𝑔) comLaw (Base‘𝑔)} |
Colors of variables: wff setvar class |
This definition is referenced by: iscsgrpALT 41652 |
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