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Definition df-mpr 8925
 Description: Define pre-multiplication on signed reals. This is a "temporary" set used in the construction of complex numbers df-c 8988, 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 8732 . 2
2 vx . . . . . . 7
32cv 1651 . . . . . 6
4 cnp 8726 . . . . . . 7
54, 4cxp 4868 . . . . . 6
63, 5wcel 1725 . . . . 5
7 vy . . . . . . 7
87cv 1651 . . . . . 6
98, 5wcel 1725 . . . . 5
106, 9wa 359 . . . 4
11 vw . . . . . . . . . . . . 13
1211cv 1651 . . . . . . . . . . . 12
13 vv . . . . . . . . . . . . 13
1413cv 1651 . . . . . . . . . . . 12
1512, 14cop 3809 . . . . . . . . . . 11
163, 15wceq 1652 . . . . . . . . . 10
17 vu . . . . . . . . . . . . 13
1817cv 1651 . . . . . . . . . . . 12
19 vf . . . . . . . . . . . . 13
2019cv 1651 . . . . . . . . . . . 12
2118, 20cop 3809 . . . . . . . . . . 11
228, 21wceq 1652 . . . . . . . . . 10
2316, 22wa 359 . . . . . . . . 9
24 vz . . . . . . . . . . 11
2524cv 1651 . . . . . . . . . 10
26 cmp 8729 . . . . . . . . . . . . 13
2712, 18, 26co 6073 . . . . . . . . . . . 12
2814, 20, 26co 6073 . . . . . . . . . . . 12
29 cpp 8728 . . . . . . . . . . . 12
3027, 28, 29co 6073 . . . . . . . . . . 11
3112, 20, 26co 6073 . . . . . . . . . . . 12
3214, 18, 26co 6073 . . . . . . . . . . . 12
3331, 32, 29co 6073 . . . . . . . . . . 11
3430, 33cop 3809 . . . . . . . . . 10
3525, 34wceq 1652 . . . . . . . . 9
3623, 35wa 359 . . . . . . . 8
3736, 19wex 1550 . . . . . . 7
3837, 17wex 1550 . . . . . 6
3938, 13wex 1550 . . . . 5
4039, 11wex 1550 . . . 4
4110, 40wa 359 . . 3
4241, 2, 7, 24coprab 6074 . 2
431, 42wceq 1652 1
 Colors of variables: wff set class This definition is referenced by:  mulsrpr  8943
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