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Definition df-plqqs 6504
 Description: Define 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. From Proposition 9-2.3 of [Gleason] p. 117. (Contributed by NM, 24-Aug-1995.)
Assertion
Ref Expression
df-plqqs
Distinct variable group:   ,,,,,,

Detailed syntax breakdown of Definition df-plqqs
StepHypRef Expression
1 cplq 6437 . 2
2 vx . . . . . . 7
32cv 1258 . . . . . 6
4 cnq 6435 . . . . . 6
53, 4wcel 1409 . . . . 5
6 vy . . . . . . 7
76cv 1258 . . . . . 6
87, 4wcel 1409 . . . . 5
95, 8wa 101 . . . 4
10 vw . . . . . . . . . . . . . 14
1110cv 1258 . . . . . . . . . . . . 13
12 vv . . . . . . . . . . . . . 14
1312cv 1258 . . . . . . . . . . . . 13
1411, 13cop 3405 . . . . . . . . . . . 12
15 ceq 6434 . . . . . . . . . . . 12
1614, 15cec 6134 . . . . . . . . . . 11
173, 16wceq 1259 . . . . . . . . . 10
18 vu . . . . . . . . . . . . . 14
1918cv 1258 . . . . . . . . . . . . 13
20 vf . . . . . . . . . . . . . 14
2120cv 1258 . . . . . . . . . . . . 13
2219, 21cop 3405 . . . . . . . . . . . 12
2322, 15cec 6134 . . . . . . . . . . 11
247, 23wceq 1259 . . . . . . . . . 10
2517, 24wa 101 . . . . . . . . 9
26 vz . . . . . . . . . . 11
2726cv 1258 . . . . . . . . . 10
28 cplpq 6431 . . . . . . . . . . . 12
2914, 22, 28co 5539 . . . . . . . . . . 11
3029, 15cec 6134 . . . . . . . . . 10
3127, 30wceq 1259 . . . . . . . . 9
3225, 31wa 101 . . . . . . . 8
3332, 20wex 1397 . . . . . . 7
3433, 18wex 1397 . . . . . 6
3534, 12wex 1397 . . . . 5
3635, 10wex 1397 . . . 4
379, 36wa 101 . . 3
3837, 2, 6, 26coprab 5540 . 2
391, 38wceq 1259 1
 Colors of variables: wff set class This definition is referenced by:  addpipqqs  6525  dmaddpq  6534
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