Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-rlreg | Structured version Visualization version 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 | RLReg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crlreg 19279 | . 2 RLReg | |
2 | vr | . . 3 | |
3 | cvv 3200 | . . 3 | |
4 | vx | . . . . . . . . 9 | |
5 | 4 | cv 1482 | . . . . . . . 8 |
6 | vy | . . . . . . . . 9 | |
7 | 6 | cv 1482 | . . . . . . . 8 |
8 | 2 | cv 1482 | . . . . . . . . 9 |
9 | cmulr 15942 | . . . . . . . . 9 | |
10 | 8, 9 | cfv 5888 | . . . . . . . 8 |
11 | 5, 7, 10 | co 6650 | . . . . . . 7 |
12 | c0g 16100 | . . . . . . . 8 | |
13 | 8, 12 | cfv 5888 | . . . . . . 7 |
14 | 11, 13 | wceq 1483 | . . . . . 6 |
15 | 7, 13 | wceq 1483 | . . . . . 6 |
16 | 14, 15 | wi 4 | . . . . 5 |
17 | cbs 15857 | . . . . . 6 | |
18 | 8, 17 | cfv 5888 | . . . . 5 |
19 | 16, 6, 18 | wral 2912 | . . . 4 |
20 | 19, 4, 18 | crab 2916 | . . 3 |
21 | 2, 3, 20 | cmpt 4729 | . 2 |
22 | 1, 21 | wceq 1483 | 1 RLReg |
Colors of variables: wff setvar class |
This definition is referenced by: rrgval 19287 |
Copyright terms: Public domain | W3C validator |