Definition df-mq 10602

Description: Define multiplication on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c 10808, and is intended to be used only by the construction. From Proposition 9-2.4 of [Gleason] p. 119. (Contributed by NM, 24-Aug-1995.) (New usage is discouraged.)

Assertion

Ref	Expression
df-mq	⊢ ·Q = (([Q] ∘ ·pQ ) ↾ (Q × Q))

Detailed syntax breakdown of Definition df-mq

Step	Hyp	Ref	Expression
1		cmq 10543	. 2 class ·Q
2		cerq 10541	. . . 4 class [Q]
3		cmpq 10536	. . . 4 class ·pQ
4	2, 3	ccom 5584	. . 3 class ([Q] ∘ ·pQ )
5		cnq 10539	. . . 4 class Q
6	5, 5	cxp 5578	. . 3 class (Q × Q)
7	4, 6	cres 5582	. 2 class (([Q] ∘ ·pQ ) ↾ (Q × Q))
8	1, 7	wceq 1539	1 wff ·Q = (([Q] ∘ ·pQ ) ↾ (Q × Q))

This definition is referenced by:  mulpqnq  10628  mulnqf  10636