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Mirrors > Home > MPE Home > Th. List > df-drngo | Structured version Visualization version Unicode version |
Description: Define the class of all division rings (sometimes called skew fields). A division ring is a unital ring where every element except the additive identity has a multiplicative inverse. (Contributed by NM, 4-Apr-2009.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-drngo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdrng 26133 |
. 2
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2 | vg |
. . . . . . 7
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3 | 2 | cv 1443 |
. . . . . 6
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4 | vh |
. . . . . . 7
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5 | 4 | cv 1443 |
. . . . . 6
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6 | 3, 5 | cop 3974 |
. . . . 5
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7 | crngo 26103 |
. . . . 5
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8 | 6, 7 | wcel 1887 |
. . . 4
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9 | 3 | crn 4835 |
. . . . . . . 8
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10 | cgi 25915 |
. . . . . . . . . 10
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11 | 3, 10 | cfv 5582 |
. . . . . . . . 9
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12 | 11 | csn 3968 |
. . . . . . . 8
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13 | 9, 12 | cdif 3401 |
. . . . . . 7
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14 | 13, 13 | cxp 4832 |
. . . . . 6
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15 | 5, 14 | cres 4836 |
. . . . 5
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16 | cgr 25914 |
. . . . 5
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17 | 15, 16 | wcel 1887 |
. . . 4
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18 | 8, 17 | wa 371 |
. . 3
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19 | 18, 2, 4 | copab 4460 |
. 2
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20 | 1, 19 | wceq 1444 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: drngoi 26135 isdivrngo 26159 isdrngo1 32195 |
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