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Mirrors > Home > ILE Home > Th. List > df-rq | Unicode version |
Description: Define reciprocal on positive fractions. It means the same thing as one divided by the argument (although we don't define full division since we will never need it). This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-2.5 of [Gleason] p. 119, who uses an asterisk to denote this unary operation. (Contributed by Jim Kingdon, 20-Sep-2019.) |
Ref | Expression |
---|---|
df-rq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crq 7219 | . 2 | |
2 | vx | . . . . . 6 | |
3 | 2 | cv 1341 | . . . . 5 |
4 | cnq 7215 | . . . . 5 | |
5 | 3, 4 | wcel 2135 | . . . 4 |
6 | vy | . . . . . 6 | |
7 | 6 | cv 1341 | . . . . 5 |
8 | 7, 4 | wcel 2135 | . . . 4 |
9 | cmq 7218 | . . . . . 6 | |
10 | 3, 7, 9 | co 5839 | . . . . 5 |
11 | c1q 7216 | . . . . 5 | |
12 | 10, 11 | wceq 1342 | . . . 4 |
13 | 5, 8, 12 | w3a 967 | . . 3 |
14 | 13, 2, 6 | copab 4039 | . 2 |
15 | 1, 14 | wceq 1342 | 1 |
Colors of variables: wff set class |
This definition is referenced by: recmulnqg 7326 |
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