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Definition df-rq 6448
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.)
Assertion
Ref Expression
df-rq *Q = {⟨𝑥, 𝑦⟩ ∣ (𝑥Q𝑦Q ∧ (𝑥 ·Q 𝑦) = 1Q)}
Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-rq
StepHypRef Expression
1 crq 6380 . 2 class *Q
2 vx . . . . . 6 setvar 𝑥
32cv 1242 . . . . 5 class 𝑥
4 cnq 6376 . . . . 5 class Q
53, 4wcel 1393 . . . 4 wff 𝑥Q
6 vy . . . . . 6 setvar 𝑦
76cv 1242 . . . . 5 class 𝑦
87, 4wcel 1393 . . . 4 wff 𝑦Q
9 cmq 6379 . . . . . 6 class ·Q
103, 7, 9co 5512 . . . . 5 class (𝑥 ·Q 𝑦)
11 c1q 6377 . . . . 5 class 1Q
1210, 11wceq 1243 . . . 4 wff (𝑥 ·Q 𝑦) = 1Q
135, 8, 12w3a 885 . . 3 wff (𝑥Q𝑦Q ∧ (𝑥 ·Q 𝑦) = 1Q)
1413, 2, 6copab 3817 . 2 class {⟨𝑥, 𝑦⟩ ∣ (𝑥Q𝑦Q ∧ (𝑥 ·Q 𝑦) = 1Q)}
151, 14wceq 1243 1 wff *Q = {⟨𝑥, 𝑦⟩ ∣ (𝑥Q𝑦Q ∧ (𝑥 ·Q 𝑦) = 1Q)}
Colors of variables: wff set class
This definition is referenced by:  recmulnqg  6487
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