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Mirrors > Home > MPE Home > Th. List > df-lpir | Structured version Visualization version Unicode version |
Description: Define the class of left principal ideal rings, rings where every left ideal has a single generator. (Contributed by Stefan O'Rear, 3-Jan-2015.) |
Ref | Expression |
---|---|
df-lpir | LPIR LIdeal LPIdeal |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clpir 19242 | . 2 LPIR | |
2 | vw | . . . . . 6 | |
3 | 2 | cv 1482 | . . . . 5 |
4 | clidl 19170 | . . . . 5 LIdeal | |
5 | 3, 4 | cfv 5888 | . . . 4 LIdeal |
6 | clpidl 19241 | . . . . 5 LPIdeal | |
7 | 3, 6 | cfv 5888 | . . . 4 LPIdeal |
8 | 5, 7 | wceq 1483 | . . 3 LIdeal LPIdeal |
9 | crg 18547 | . . 3 | |
10 | 8, 2, 9 | crab 2916 | . 2 LIdeal LPIdeal |
11 | 1, 10 | wceq 1483 | 1 LPIR LIdeal LPIdeal |
Colors of variables: wff setvar class |
This definition is referenced by: islpir 19249 |
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