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Mirrors > Home > MPE Home > Th. List > df-subg | Structured version Visualization version Unicode version |
Description: Define a subgroup of a group as a set of elements that is a group in its own right. Equivalently (issubg2 16832), a subgroup is a subset of the group that is closed for the group internal operation (see subgcl 16827), contains the neutral element of the group (see subg0 16823) and contains the inverses for all of its elements (see subginvcl 16826). (Contributed by Mario Carneiro, 2-Dec-2014.) |
Ref | Expression |
---|---|
df-subg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csubg 16811 |
. 2
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2 | vw |
. . 3
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3 | cgrp 16669 |
. . 3
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4 | 2 | cv 1443 |
. . . . . 6
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5 | vs |
. . . . . . 7
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6 | 5 | cv 1443 |
. . . . . 6
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7 | cress 15122 |
. . . . . 6
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8 | 4, 6, 7 | co 6290 |
. . . . 5
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9 | 8, 3 | wcel 1887 |
. . . 4
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10 | cbs 15121 |
. . . . . 6
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11 | 4, 10 | cfv 5582 |
. . . . 5
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12 | 11 | cpw 3951 |
. . . 4
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13 | 9, 5, 12 | crab 2741 |
. . 3
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14 | 2, 3, 13 | cmpt 4461 |
. 2
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15 | 1, 14 | wceq 1444 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: issubg 16817 |
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