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Definition df-mpq 6329
Description: Define pre-multiplication on positive fractions. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-2.4 of [Gleason] p. 119. (Contributed by NM, 28-Aug-1995.)
Assertion
Ref Expression
df-mpq ·pQ = (x (N × N), y (N × N) ↦ ⟨((1stx) ·N (1sty)), ((2ndx) ·N (2ndy))⟩)
Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-mpq
StepHypRef Expression
1 cmpq 6261 . 2 class ·pQ
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 cnpi 6256 . . . 4 class N
54, 4cxp 4286 . . 3 class (N × N)
62cv 1241 . . . . . 6 class x
7 c1st 5707 . . . . . 6 class 1st
86, 7cfv 4845 . . . . 5 class (1stx)
93cv 1241 . . . . . 6 class y
109, 7cfv 4845 . . . . 5 class (1sty)
11 cmi 6258 . . . . 5 class ·N
128, 10, 11co 5455 . . . 4 class ((1stx) ·N (1sty))
13 c2nd 5708 . . . . . 6 class 2nd
146, 13cfv 4845 . . . . 5 class (2ndx)
159, 13cfv 4845 . . . . 5 class (2ndy)
1614, 15, 11co 5455 . . . 4 class ((2ndx) ·N (2ndy))
1712, 16cop 3370 . . 3 class ⟨((1stx) ·N (1sty)), ((2ndx) ·N (2ndy))⟩
182, 3, 5, 5, 17cmpt2 5457 . 2 class (x (N × N), y (N × N) ↦ ⟨((1stx) ·N (1sty)), ((2ndx) ·N (2ndy))⟩)
191, 18wceq 1242 1 wff ·pQ = (x (N × N), y (N × N) ↦ ⟨((1stx) ·N (1sty)), ((2ndx) ·N (2ndy))⟩)
Colors of variables: wff set class
This definition is referenced by:  dfmpq2  6339  mulpipq2  6355
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