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Definition df-rq 6422
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  e.  Q.  /\  y  e. 
Q.  /\  ( x  .Q  y )  =  1Q ) }
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-rq
StepHypRef Expression
1 crq 6354 . 2  class  *Q
2 vx . . . . . 6  setvar  x
32cv 1242 . . . . 5  class  x
4 cnq 6350 . . . . 5  class  Q.
53, 4wcel 1393 . . . 4  wff  x  e. 
Q.
6 vy . . . . . 6  setvar  y
76cv 1242 . . . . 5  class  y
87, 4wcel 1393 . . . 4  wff  y  e. 
Q.
9 cmq 6353 . . . . . 6  class  .Q
103, 7, 9co 5490 . . . . 5  class  ( x  .Q  y )
11 c1q 6351 . . . . 5  class  1Q
1210, 11wceq 1243 . . . 4  wff  ( x  .Q  y )  =  1Q
135, 8, 12w3a 885 . . 3  wff  ( x  e.  Q.  /\  y  e.  Q.  /\  ( x  .Q  y )  =  1Q )
1413, 2, 6copab 3814 . 2  class  { <. x ,  y >.  |  ( x  e.  Q.  /\  y  e.  Q.  /\  (
x  .Q  y )  =  1Q ) }
151, 14wceq 1243 1  wff  *Q  =  { <. x ,  y
>.  |  ( x  e.  Q.  /\  y  e. 
Q.  /\  ( x  .Q  y )  =  1Q ) }
Colors of variables: wff set class
This definition is referenced by:  recmulnqg  6461
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