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

Definition df-mr 9457
Description: Define multiplication on signed reals. This is a "temporary" set used in the construction of complex numbers df-c 9519, 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-mr
Distinct variable group:   , , , , , ,

Detailed syntax breakdown of Definition df-mr
StepHypRef Expression
1 cmr 9269 . 2
2 vx . . . . . . 7
32cv 1394 . . . . . 6
4 cnr 9264 . . . . . 6
53, 4wcel 1818 . . . . 5
6 vy . . . . . . 7
76cv 1394 . . . . . 6
87, 4wcel 1818 . . . . 5
95, 8wa 369 . . . 4
10 vw . . . . . . . . . . . . . 14
1110cv 1394 . . . . . . . . . . . . 13
12 vv . . . . . . . . . . . . . 14
1312cv 1394 . . . . . . . . . . . . 13
1411, 13cop 4035 . . . . . . . . . . . 12
15 cer 9263 . . . . . . . . . . . 12
1614, 15cec 7328 . . . . . . . . . . 11
173, 16wceq 1395 . . . . . . . . . 10
18 vu . . . . . . . . . . . . . 14
1918cv 1394 . . . . . . . . . . . . 13
20 vf . . . . . . . . . . . . . 14
2120cv 1394 . . . . . . . . . . . . 13
2219, 21cop 4035 . . . . . . . . . . . 12
2322, 15cec 7328 . . . . . . . . . . 11
247, 23wceq 1395 . . . . . . . . . 10
2517, 24wa 369 . . . . . . . . 9
26 vz . . . . . . . . . . 11
2726cv 1394 . . . . . . . . . 10
28 cmp 9261 . . . . . . . . . . . . . 14
2911, 19, 28co 6296 . . . . . . . . . . . . 13
3013, 21, 28co 6296 . . . . . . . . . . . . 13
31 cpp 9260 . . . . . . . . . . . . 13
3229, 30, 31co 6296 . . . . . . . . . . . 12
3311, 21, 28co 6296 . . . . . . . . . . . . 13
3413, 19, 28co 6296 . . . . . . . . . . . . 13
3533, 34, 31co 6296 . . . . . . . . . . . 12
3632, 35cop 4035 . . . . . . . . . . 11
3736, 15cec 7328 . . . . . . . . . 10
3827, 37wceq 1395 . . . . . . . . 9
3925, 38wa 369 . . . . . . . 8
4039, 20wex 1612 . . . . . . 7
4140, 18wex 1612 . . . . . 6
4241, 12wex 1612 . . . . 5
4342, 10wex 1612 . . . 4
449, 43wa 369 . . 3
4544, 2, 6, 26coprab 6297 . 2
461, 45wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  mulsrpr  9474  dmmulsr  9484
  Copyright terms: Public domain W3C validator