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Definition df-plpq 6442
 Description: Define pre-addition 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. This "pre-addition" operation works directly with ordered pairs of integers. The actual positive fraction addition (df-plqqs 6447) works with the equivalence classes of these ordered pairs determined by the equivalence relation (df-enq 6445). (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.)
Assertion
Ref Expression
df-plpq
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-plpq
StepHypRef Expression
1 cplpq 6374 . 2
2 vx . . 3
3 vy . . 3
4 cnpi 6370 . . . 4
54, 4cxp 4343 . . 3
62cv 1242 . . . . . . 7
7 c1st 5765 . . . . . . 7
86, 7cfv 4902 . . . . . 6
93cv 1242 . . . . . . 7
10 c2nd 5766 . . . . . . 7
119, 10cfv 4902 . . . . . 6
12 cmi 6372 . . . . . 6
138, 11, 12co 5512 . . . . 5
149, 7cfv 4902 . . . . . 6
156, 10cfv 4902 . . . . . 6
1614, 15, 12co 5512 . . . . 5
17 cpli 6371 . . . . 5
1813, 16, 17co 5512 . . . 4
1915, 11, 12co 5512 . . . 4
2018, 19cop 3378 . . 3
212, 3, 5, 5, 20cmpt2 5514 . 2
221, 21wceq 1243 1
 Colors of variables: wff set class This definition is referenced by:  dfplpq2  6452
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