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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 6539) works with the equivalence classes of these ordered pairs determined by the equivalence relation (df-enq 6537). (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.) |
Ref | Expression |
---|---|
df-plpq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cplpq 6466 | . 2 | |
2 | vx | . . 3 | |
3 | vy | . . 3 | |
4 | cnpi 6462 | . . . 4 | |
5 | 4, 4 | cxp 4361 | . . 3 |
6 | 2 | cv 1283 | . . . . . . 7 |
7 | c1st 5785 | . . . . . . 7 | |
8 | 6, 7 | cfv 4922 | . . . . . 6 |
9 | 3 | cv 1283 | . . . . . . 7 |
10 | c2nd 5786 | . . . . . . 7 | |
11 | 9, 10 | cfv 4922 | . . . . . 6 |
12 | cmi 6464 | . . . . . 6 | |
13 | 8, 11, 12 | co 5532 | . . . . 5 |
14 | 9, 7 | cfv 4922 | . . . . . 6 |
15 | 6, 10 | cfv 4922 | . . . . . 6 |
16 | 14, 15, 12 | co 5532 | . . . . 5 |
17 | cpli 6463 | . . . . 5 | |
18 | 13, 16, 17 | co 5532 | . . . 4 |
19 | 15, 11, 12 | co 5532 | . . . 4 |
20 | 18, 19 | cop 3401 | . . 3 |
21 | 2, 3, 5, 5, 20 | cmpt2 5534 | . 2 |
22 | 1, 21 | wceq 1284 | 1 |
Colors of variables: wff set class |
This definition is referenced by: dfplpq2 6544 |
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