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Mirrors > Home > ILE Home > Th. List > df-mpq | Unicode version |
Description: Define pre-multiplication on positive fractions. This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. From Proposition 9-2.4 of [Gleason] p. 119. (Contributed by NM, 28-Aug-1995.) |
Ref | Expression |
---|---|
df-mpq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmpq 6986 |
. 2
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2 | vx |
. . 3
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3 | vy |
. . 3
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4 | cnpi 6981 |
. . . 4
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5 | 4, 4 | cxp 4475 |
. . 3
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6 | 2 | cv 1298 |
. . . . . 6
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7 | c1st 5967 |
. . . . . 6
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8 | 6, 7 | cfv 5059 |
. . . . 5
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9 | 3 | cv 1298 |
. . . . . 6
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10 | 9, 7 | cfv 5059 |
. . . . 5
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11 | cmi 6983 |
. . . . 5
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12 | 8, 10, 11 | co 5706 |
. . . 4
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13 | c2nd 5968 |
. . . . . 6
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14 | 6, 13 | cfv 5059 |
. . . . 5
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15 | 9, 13 | cfv 5059 |
. . . . 5
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16 | 14, 15, 11 | co 5706 |
. . . 4
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17 | 12, 16 | cop 3477 |
. . 3
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18 | 2, 3, 5, 5, 17 | cmpo 5708 |
. 2
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19 | 1, 18 | wceq 1299 |
1
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Colors of variables: wff set class |
This definition is referenced by: dfmpq2 7064 mulpipq2 7080 |
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