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Definition df-plpq 9307
Description: Define pre-addition on positive fractions. This is a "temporary" set used in the construction of complex numbers df-c 9519, and is intended to be used only by the construction. This "pre-addition" operation works directly with ordered pairs of integers. The actual positive fraction addition (df-plq 9313) works with the equivalence classes of these ordered pairs determined by the equivalence relation (df-enq 9310). (Analogous remarks apply to the other "pre-" operations in the complex number construction that follows.) From Proposition 9-2.3 of [Gleason] p. 117. (Contributed by NM, 28-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-plpq
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-plpq
StepHypRef Expression
1 cplpq 9247 . 2
2 vx . . 3
3 vy . . 3
4 cnpi 9243 . . . 4
54, 4cxp 5002 . . 3
62cv 1394 . . . . . . 7
7 c1st 6798 . . . . . . 7
86, 7cfv 5593 . . . . . 6
93cv 1394 . . . . . . 7
10 c2nd 6799 . . . . . . 7
119, 10cfv 5593 . . . . . 6
12 cmi 9245 . . . . . 6
138, 11, 12co 6296 . . . . 5
149, 7cfv 5593 . . . . . 6
156, 10cfv 5593 . . . . . 6
1614, 15, 12co 6296 . . . . 5
17 cpli 9244 . . . . 5
1813, 16, 17co 6296 . . . 4
1915, 11, 12co 6296 . . . 4
2018, 19cop 4035 . . 3
212, 3, 5, 5, 20cmpt2 6298 . 2
221, 21wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  addpipq2  9335  addpqnq  9337  addpqf  9343
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