Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-plr Structured version   Unicode version

Definition df-plr 8926
 Description: Define addition on signed reals. This is a "temporary" set used in the construction of complex numbers df-c 8986, 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.) (New usage is discouraged.)
Assertion
Ref Expression
df-plr
Distinct variable group:   ,,,,,,

Detailed syntax breakdown of Definition df-plr
StepHypRef Expression
1 cplr 8736 . 2
2 vx . . . . . . 7
32cv 1651 . . . . . 6
4 cnr 8732 . . . . . 6
53, 4wcel 1725 . . . . 5
6 vy . . . . . . 7
76cv 1651 . . . . . 6
87, 4wcel 1725 . . . . 5
95, 8wa 359 . . . 4
10 vw . . . . . . . . . . . . . 14
1110cv 1651 . . . . . . . . . . . . 13
12 vv . . . . . . . . . . . . . 14
1312cv 1651 . . . . . . . . . . . . 13
1411, 13cop 3809 . . . . . . . . . . . 12
15 cer 8731 . . . . . . . . . . . 12
1614, 15cec 6895 . . . . . . . . . . 11
173, 16wceq 1652 . . . . . . . . . 10
18 vu . . . . . . . . . . . . . 14
1918cv 1651 . . . . . . . . . . . . 13
20 vf . . . . . . . . . . . . . 14
2120cv 1651 . . . . . . . . . . . . 13
2219, 21cop 3809 . . . . . . . . . . . 12
2322, 15cec 6895 . . . . . . . . . . 11
247, 23wceq 1652 . . . . . . . . . 10
2517, 24wa 359 . . . . . . . . 9
26 vz . . . . . . . . . . 11
2726cv 1651 . . . . . . . . . 10
28 cplpr 8729 . . . . . . . . . . . 12
2914, 22, 28co 6073 . . . . . . . . . . 11
3029, 15cec 6895 . . . . . . . . . 10
3127, 30wceq 1652 . . . . . . . . 9
3225, 31wa 359 . . . . . . . 8
3332, 20wex 1550 . . . . . . 7
3433, 18wex 1550 . . . . . 6
3534, 12wex 1550 . . . . 5
3635, 10wex 1550 . . . 4
379, 36wa 359 . . 3
3837, 2, 6, 26coprab 6074 . 2
391, 38wceq 1652 1
 Colors of variables: wff set class This definition is referenced by:  addsrpr  8940  dmaddsr  8950
 Copyright terms: Public domain W3C validator