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Mirrors > Home > MPE Home > Th. List > df-nzr | Structured version Visualization version 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 | NzRing |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnzr 19257 | . 2 NzRing | |
2 | vr | . . . . . 6 | |
3 | 2 | cv 1482 | . . . . 5 |
4 | cur 18501 | . . . . 5 | |
5 | 3, 4 | cfv 5888 | . . . 4 |
6 | c0g 16100 | . . . . 5 | |
7 | 3, 6 | cfv 5888 | . . . 4 |
8 | 5, 7 | wne 2794 | . . 3 |
9 | crg 18547 | . . 3 | |
10 | 8, 2, 9 | crab 2916 | . 2 |
11 | 1, 10 | wceq 1483 | 1 NzRing |
Colors of variables: wff setvar class |
This definition is referenced by: isnzr 19259 |
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