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Mirrors > Home > MPE Home > Th. List > df-denom | Structured version Visualization version Unicode version |
Description: The canonical denominator of a rational is the denominator of the rational's reduced fraction representation (no common factors, denominator positive). (Contributed by Stefan O'Rear, 13-Sep-2014.) |
Ref | Expression |
---|---|
df-denom | denom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdenom 15442 | . 2 denom | |
2 | vy | . . 3 | |
3 | cq 11788 | . . 3 | |
4 | vx | . . . . . . . . . 10 | |
5 | 4 | cv 1482 | . . . . . . . . 9 |
6 | c1st 7166 | . . . . . . . . 9 | |
7 | 5, 6 | cfv 5888 | . . . . . . . 8 |
8 | c2nd 7167 | . . . . . . . . 9 | |
9 | 5, 8 | cfv 5888 | . . . . . . . 8 |
10 | cgcd 15216 | . . . . . . . 8 | |
11 | 7, 9, 10 | co 6650 | . . . . . . 7 |
12 | c1 9937 | . . . . . . 7 | |
13 | 11, 12 | wceq 1483 | . . . . . 6 |
14 | 2 | cv 1482 | . . . . . . 7 |
15 | cdiv 10684 | . . . . . . . 8 | |
16 | 7, 9, 15 | co 6650 | . . . . . . 7 |
17 | 14, 16 | wceq 1483 | . . . . . 6 |
18 | 13, 17 | wa 384 | . . . . 5 |
19 | cz 11377 | . . . . . 6 | |
20 | cn 11020 | . . . . . 6 | |
21 | 19, 20 | cxp 5112 | . . . . 5 |
22 | 18, 4, 21 | crio 6610 | . . . 4 |
23 | 22, 8 | cfv 5888 | . . 3 |
24 | 2, 3, 23 | cmpt 4729 | . 2 |
25 | 1, 24 | wceq 1483 | 1 denom |
Colors of variables: wff setvar class |
This definition is referenced by: qdenval 15446 fden 15451 |
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