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Mirrors > Home > ILE Home > Th. List > df-rlreg | Unicode version |
Description: Define the set of left-regular elements in a ring as those elements which are not left zero divisors, meaning that multiplying a nonzero element on the left by a left-regular element gives a nonzero product. (Contributed by Stefan O'Rear, 22-Mar-2015.) |
Ref | Expression |
---|---|
df-rlreg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crlreg 13735 |
. 2
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2 | vr |
. . 3
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3 | cvv 2760 |
. . 3
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4 | vx |
. . . . . . . . 9
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5 | 4 | cv 1363 |
. . . . . . . 8
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6 | vy |
. . . . . . . . 9
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7 | 6 | cv 1363 |
. . . . . . . 8
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8 | 2 | cv 1363 |
. . . . . . . . 9
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9 | cmulr 12686 |
. . . . . . . . 9
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10 | 8, 9 | cfv 5246 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() |
11 | 5, 7, 10 | co 5910 |
. . . . . . 7
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12 | c0g 12857 |
. . . . . . . 8
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13 | 8, 12 | cfv 5246 |
. . . . . . 7
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14 | 11, 13 | wceq 1364 |
. . . . . 6
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15 | 7, 13 | wceq 1364 |
. . . . . 6
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16 | 14, 15 | wi 4 |
. . . . 5
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17 | cbs 12608 |
. . . . . 6
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18 | 8, 17 | cfv 5246 |
. . . . 5
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19 | 16, 6, 18 | wral 2472 |
. . . 4
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20 | 19, 4, 18 | crab 2476 |
. . 3
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21 | 2, 3, 20 | cmpt 4090 |
. 2
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22 | 1, 21 | wceq 1364 |
1
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Colors of variables: wff set class |
This definition is referenced by: rrgmex 13741 rrgval 13742 |
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