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Definition df-plr 6813
 Description: Define addition on signed reals. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-4.3 of [Gleason] p. 126. (Contributed by NM, 25-Aug-1995.)
Assertion
Ref Expression
df-plr
Distinct variable group:   ,,,,,,

Detailed syntax breakdown of Definition df-plr
StepHypRef Expression
1 cplr 6399 . 2
2 vx . . . . . . 7
32cv 1242 . . . . . 6
4 cnr 6395 . . . . . 6
53, 4wcel 1393 . . . . 5
6 vy . . . . . . 7
76cv 1242 . . . . . 6
87, 4wcel 1393 . . . . 5
95, 8wa 97 . . . 4
10 vw . . . . . . . . . . . . . 14
1110cv 1242 . . . . . . . . . . . . 13
12 vv . . . . . . . . . . . . . 14
1312cv 1242 . . . . . . . . . . . . 13
1411, 13cop 3378 . . . . . . . . . . . 12
15 cer 6394 . . . . . . . . . . . 12
1614, 15cec 6104 . . . . . . . . . . 11
173, 16wceq 1243 . . . . . . . . . 10
18 vu . . . . . . . . . . . . . 14
1918cv 1242 . . . . . . . . . . . . 13
20 vf . . . . . . . . . . . . . 14
2120cv 1242 . . . . . . . . . . . . 13
2219, 21cop 3378 . . . . . . . . . . . 12
2322, 15cec 6104 . . . . . . . . . . 11
247, 23wceq 1243 . . . . . . . . . 10
2517, 24wa 97 . . . . . . . . 9
26 vz . . . . . . . . . . 11
2726cv 1242 . . . . . . . . . 10
28 cpp 6391 . . . . . . . . . . . . 13
2911, 19, 28co 5512 . . . . . . . . . . . 12
3013, 21, 28co 5512 . . . . . . . . . . . 12
3129, 30cop 3378 . . . . . . . . . . 11
3231, 15cec 6104 . . . . . . . . . 10
3327, 32wceq 1243 . . . . . . . . 9
3425, 33wa 97 . . . . . . . 8
3534, 20wex 1381 . . . . . . 7
3635, 18wex 1381 . . . . . 6
3736, 12wex 1381 . . . . 5
3837, 10wex 1381 . . . 4
399, 38wa 97 . . 3
4039, 2, 6, 26coprab 5513 . 2
411, 40wceq 1243 1
 Colors of variables: wff set class This definition is referenced by:  addsrpr  6830
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