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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 ) )