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Definition df-rq 6336
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⟩ ∣ (x Q y Q (x ·Q y) = 1Q)}
Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-rq
StepHypRef Expression
1 crq 6268 . 2 class *Q
2 vx . . . . . 6 setvar x
32cv 1241 . . . . 5 class x
4 cnq 6264 . . . . 5 class Q
53, 4wcel 1390 . . . 4 wff x Q
6 vy . . . . . 6 setvar y
76cv 1241 . . . . 5 class y
87, 4wcel 1390 . . . 4 wff y Q
9 cmq 6267 . . . . . 6 class ·Q
103, 7, 9co 5455 . . . . 5 class (x ·Q y)
11 c1q 6265 . . . . 5 class 1Q
1210, 11wceq 1242 . . . 4 wff (x ·Q y) = 1Q
135, 8, 12w3a 884 . . 3 wff (x Q y Q (x ·Q y) = 1Q)
1413, 2, 6copab 3808 . 2 class {⟨x, y⟩ ∣ (x Q y Q (x ·Q y) = 1Q)}
151, 14wceq 1242 1 wff *Q = {⟨x, y⟩ ∣ (x Q y Q (x ·Q y) = 1Q)}
Colors of variables: wff set class
This definition is referenced by:  recmulnqg  6375
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