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

Definition df-mpr 8560
 Description: Define pre-multiplication on signed reals. This is a "temporary" set used in the construction of complex numbers df-c 8623, and is intended to be used only by the construction. From Proposition 9-4.1 of [Gleason] p. 126. (Contributed by NM, 3-Sep-1995.) (New usage is discouraged.)
Assertion
Ref Expression
df-mpr
Distinct variable group:   ,,,,,,

Detailed syntax breakdown of Definition df-mpr
StepHypRef Expression
1 cmpr 8367 . 2
2 vx . . . . . . 7
32cv 1618 . . . . . 6
4 cnp 8361 . . . . . . 7
54, 4cxp 4578 . . . . . 6
63, 5wcel 1621 . . . . 5
7 vy . . . . . . 7
87cv 1618 . . . . . 6
98, 5wcel 1621 . . . . 5
106, 9wa 360 . . . 4
11 vw . . . . . . . . . . . . 13
1211cv 1618 . . . . . . . . . . . 12
13 vv . . . . . . . . . . . . 13
1413cv 1618 . . . . . . . . . . . 12
1512, 14cop 3547 . . . . . . . . . . 11
163, 15wceq 1619 . . . . . . . . . 10
17 vu . . . . . . . . . . . . 13
1817cv 1618 . . . . . . . . . . . 12
19 vf . . . . . . . . . . . . 13
2019cv 1618 . . . . . . . . . . . 12
2118, 20cop 3547 . . . . . . . . . . 11
228, 21wceq 1619 . . . . . . . . . 10
2316, 22wa 360 . . . . . . . . 9
24 vz . . . . . . . . . . 11
2524cv 1618 . . . . . . . . . 10
26 cmp 8364 . . . . . . . . . . . . 13
2712, 18, 26co 5710 . . . . . . . . . . . 12
2814, 20, 26co 5710 . . . . . . . . . . . 12
29 cpp 8363 . . . . . . . . . . . 12
3027, 28, 29co 5710 . . . . . . . . . . 11
3112, 20, 26co 5710 . . . . . . . . . . . 12
3214, 18, 26co 5710 . . . . . . . . . . . 12
3331, 32, 29co 5710 . . . . . . . . . . 11
3430, 33cop 3547 . . . . . . . . . 10
3525, 34wceq 1619 . . . . . . . . 9
3623, 35wa 360 . . . . . . . 8
3736, 19wex 1537 . . . . . . 7
3837, 17wex 1537 . . . . . 6
3938, 13wex 1537 . . . . 5
4039, 11wex 1537 . . . 4
4110, 40wa 360 . . 3
4241, 2, 7, 24copab2 5711 . 2
431, 42wceq 1619 1
 Colors of variables: wff set class This definition is referenced by:  mulsrpr  8578
 Copyright terms: Public domain W3C validator