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

Definition df-erq 10324
Description: Define a convenience function that "reduces" a fraction to lowest terms. Note that in this form, it is not obviously a function; we prove this in nqerf 10341. (Contributed by NM, 27-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-erq [Q] = ( ~Q ∩ ((N × N) × Q))

Detailed syntax breakdown of Definition df-erq
StepHypRef Expression
1 cerq 10265 . 2 class [Q]
2 ceq 10262 . . 3 class ~Q
3 cnpi 10255 . . . . 5 class N
43, 3cxp 5547 . . . 4 class (N × N)
5 cnq 10263 . . . 4 class Q
64, 5cxp 5547 . . 3 class ((N × N) × Q)
72, 6cin 3934 . 2 class ( ~Q ∩ ((N × N) × Q))
81, 7wceq 1528 1 wff [Q] = ( ~Q ∩ ((N × N) × Q))
Colors of variables: wff setvar class
This definition is referenced by:  nqerf  10341  nqerrel  10343  nqerid  10344
  Copyright terms: Public domain W3C validator