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Mirrors > Home > ILE Home > Th. List > df-mgm | Unicode version |
Description: A magma is a set equipped with an everywhere defined internal operation. Definition 1 in [BourbakiAlg1] p. 1, or definition of a groupoid in section I.1 of [Bruck] p. 1. Note: The term "groupoid" is now widely used to refer to other objects: (small) categories all of whose morphisms are invertible, or groups with a partial function replacing the binary operation. Therefore, we will only use the term "magma" for the present notion in set.mm. (Contributed by FL, 2-Nov-2009.) (Revised by AV, 6-Jan-2020.) |
Ref | Expression |
---|---|
df-mgm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmgm 12662 |
. 2
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2 | vx |
. . . . . . . . . 10
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3 | 2 | cv 1352 |
. . . . . . . . 9
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4 | vy |
. . . . . . . . . 10
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5 | 4 | cv 1352 |
. . . . . . . . 9
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6 | vo |
. . . . . . . . . 10
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7 | 6 | cv 1352 |
. . . . . . . . 9
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8 | 3, 5, 7 | co 5869 |
. . . . . . . 8
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9 | vb |
. . . . . . . . 9
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10 | 9 | cv 1352 |
. . . . . . . 8
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11 | 8, 10 | wcel 2148 |
. . . . . . 7
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12 | 11, 4, 10 | wral 2455 |
. . . . . 6
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13 | 12, 2, 10 | wral 2455 |
. . . . 5
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14 | vg |
. . . . . . 7
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15 | 14 | cv 1352 |
. . . . . 6
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16 | cplusg 12515 |
. . . . . 6
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17 | 15, 16 | cfv 5212 |
. . . . 5
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18 | 13, 6, 17 | wsbc 2962 |
. . . 4
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19 | cbs 12442 |
. . . . 5
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20 | 15, 19 | cfv 5212 |
. . . 4
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21 | 18, 9, 20 | wsbc 2962 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21, 14 | cab 2163 |
. 2
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23 | 1, 22 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: ismgm 12665 |
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