Metamath Proof Explorer


Definition df-mq

Description: Define multiplication on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c , 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.)

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

Detailed syntax breakdown

Step Hyp Ref Expression
0 cmq ·Q
1 cerq [Q]
2 cmpq ·pQ
3 1 2 ccom ( [Q] ∘ ·pQ )
4 cnq Q
5 4 4 cxp ( Q × Q )
6 3 5 cres ( ( [Q] ∘ ·pQ ) ↾ ( Q × Q ) )
7 0 6 wceq ·Q = ( ( [Q] ∘ ·pQ ) ↾ ( Q × Q ) )