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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  N.  X.  N. ,  N. 
X.  N.  |->  <. 1st `  .N  1st `  ,  2nd `  .N  2nd `  >.
Distinct variable group:   ,

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