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

Definition df-plq 10528
Description: Define addition on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c 10735, and is intended to be used only by the construction. From Proposition 9-2.3 of [Gleason] p. 117. (Contributed by NM, 24-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-plq +Q = (([Q] ∘ +pQ ) ↾ (Q × Q))

Detailed syntax breakdown of Definition df-plq
StepHypRef Expression
1 cplq 10469 . 2 class +Q
2 cerq 10468 . . . 4 class [Q]
3 cplpq 10462 . . . 4 class +pQ
42, 3ccom 5555 . . 3 class ([Q] ∘ +pQ )
5 cnq 10466 . . . 4 class Q
65, 5cxp 5549 . . 3 class (Q × Q)
74, 6cres 5553 . 2 class (([Q] ∘ +pQ ) ↾ (Q × Q))
81, 7wceq 1543 1 wff +Q = (([Q] ∘ +pQ ) ↾ (Q × Q))
Colors of variables: wff setvar class
This definition is referenced by:  addpqnq  10552  addnqf  10562
  Copyright terms: Public domain W3C validator