MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-rq Structured version   Visualization version   GIF version

Definition df-rq 9777
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.)
Assertion
Ref Expression
df-rq *Q = ( ·Q “ {1Q})

Detailed syntax breakdown of Definition df-rq
StepHypRef Expression
1 crq 9717 . 2 class *Q
2 cmq 9716 . . . 4 class ·Q
32ccnv 5142 . . 3 class ·Q
4 c1q 9713 . . . 4 class 1Q
54csn 4210 . . 3 class {1Q}
63, 5cima 5146 . 2 class ( ·Q “ {1Q})
71, 6wceq 1523 1 wff *Q = ( ·Q “ {1Q})
Colors of variables: wff setvar class
This definition is referenced by:  recmulnq  9824  dmrecnq  9828
  Copyright terms: Public domain W3C validator