Definition df-erq 10600

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 10617. (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

Step	Hyp	Ref	Expression
1		cerq 10541	. 2 class [Q]
2		ceq 10538	. . 3 class ~Q
3		cnpi 10531	. . . . 5 class N
4	3, 3	cxp 5578	. . . 4 class (N × N)
5		cnq 10539	. . . 4 class Q
6	4, 5	cxp 5578	. . 3 class ((N × N) × Q)
7	2, 6	cin 3882	. 2 class ( ~Q ∩ ((N × N) × Q))
8	1, 7	wceq 1539	1 wff [Q] = ( ~Q ∩ ((N × N) × Q))

This definition is referenced by:  nqerf  10617  nqerrel  10619  nqerid  10620