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Mirrors > Home > MPE Home > Th. List > df-drng | Structured version Visualization version Unicode version |
Description: Define class of all division rings. A division ring is a ring in which the set of units is exactly the nonzero elements of the ring. (Contributed by NM, 18-Oct-2012.) |
Ref | Expression |
---|---|
df-drng |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdr 18024 |
. 2
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2 | vr |
. . . . . 6
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3 | 2 | cv 1454 |
. . . . 5
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4 | cui 17916 |
. . . . 5
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5 | 3, 4 | cfv 5601 |
. . . 4
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6 | cbs 15170 |
. . . . . 6
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7 | 3, 6 | cfv 5601 |
. . . . 5
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8 | c0g 15387 |
. . . . . . 7
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9 | 3, 8 | cfv 5601 |
. . . . . 6
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10 | 9 | csn 3980 |
. . . . 5
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11 | 7, 10 | cdif 3413 |
. . . 4
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12 | 5, 11 | wceq 1455 |
. . 3
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13 | crg 17829 |
. . 3
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14 | 12, 2, 13 | crab 2753 |
. 2
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15 | 1, 14 | wceq 1455 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: isdrng 18028 |
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