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Mirrors > Home > MPE Home > Th. List > df-rq | Structured version Visualization version GIF 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 df-c 9980, 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 NM, 6-Mar-1996.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-rq | ⊢ *_{Q} = (^{◡} ·_{Q} “ {1_{Q}}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crq 9717 | . 2 class *_{Q} | |
2 | cmq 9716 | . . . 4 class ·_{Q} | |
3 | 2 | ccnv 5142 | . . 3 class ^{◡} ·_{Q} |
4 | c1q 9713 | . . . 4 class 1_{Q} | |
5 | 4 | csn 4210 | . . 3 class {1_{Q}} |
6 | 3, 5 | cima 5146 | . 2 class (^{◡} ·_{Q} “ {1_{Q}}) |
7 | 1, 6 | wceq 1523 | 1 wff *_{Q} = (^{◡} ·_{Q} “ {1_{Q}}) |
Colors of variables: wff setvar class |
This definition is referenced by: recmulnq 9824 dmrecnq 9828 |
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