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Mirrors > Home > ILE Home > Th. List > df-nzr | Unicode version |
Description: A nonzero or nontrivial ring is a ring with at least two values, or equivalently where 1 and 0 are different. (Contributed by Stefan O'Rear, 24-Feb-2015.) |
Ref | Expression |
---|---|
df-nzr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnzr 13254 |
. 2
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2 | vr |
. . . . . 6
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3 | 2 | cv 1352 |
. . . . 5
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4 | cur 13073 |
. . . . 5
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5 | 3, 4 | cfv 5215 |
. . . 4
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6 | c0g 12693 |
. . . . 5
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7 | 3, 6 | cfv 5215 |
. . . 4
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8 | 5, 7 | wne 2347 |
. . 3
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9 | crg 13110 |
. . 3
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10 | 8, 2, 9 | crab 2459 |
. 2
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11 | 1, 10 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: isnzr 13256 nzrring 13258 |
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