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Mirrors > Home > ILE Home > Th. List > df-domn | Unicode version |
Description: A domain is a nonzero ring in which there are no nontrivial zero divisors. (Contributed by Mario Carneiro, 28-Mar-2015.) |
Ref | Expression |
---|---|
df-domn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdomn 13736 |
. 2
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2 | vx |
. . . . . . . . . . 11
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3 | 2 | cv 1363 |
. . . . . . . . . 10
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4 | vy |
. . . . . . . . . . 11
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5 | 4 | cv 1363 |
. . . . . . . . . 10
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6 | vr |
. . . . . . . . . . . 12
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7 | 6 | cv 1363 |
. . . . . . . . . . 11
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8 | cmulr 12686 |
. . . . . . . . . . 11
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9 | 7, 8 | cfv 5246 |
. . . . . . . . . 10
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10 | 3, 5, 9 | co 5910 |
. . . . . . . . 9
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11 | vz |
. . . . . . . . . 10
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12 | 11 | cv 1363 |
. . . . . . . . 9
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13 | 10, 12 | wceq 1364 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 2, 11 | weq 1514 |
. . . . . . . . 9
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15 | 4, 11 | weq 1514 |
. . . . . . . . 9
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16 | 14, 15 | wo 709 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 13, 16 | wi 4 |
. . . . . . 7
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18 | vb |
. . . . . . . 8
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19 | 18 | cv 1363 |
. . . . . . 7
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20 | 17, 4, 19 | wral 2472 |
. . . . . 6
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21 | 20, 2, 19 | wral 2472 |
. . . . 5
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22 | c0g 12857 |
. . . . . 6
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23 | 7, 22 | cfv 5246 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
24 | 21, 11, 23 | wsbc 2985 |
. . . 4
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25 | cbs 12608 |
. . . . 5
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26 | 7, 25 | cfv 5246 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() |
27 | 24, 18, 26 | wsbc 2985 |
. . 3
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28 | cnzr 13659 |
. . 3
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29 | 27, 6, 28 | crab 2476 |
. 2
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30 | 1, 29 | wceq 1364 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: isdomn 13749 |
Copyright terms: Public domain | W3C validator |