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Mirrors > Home > ILE Home > Th. List > df-rpcxp | Unicode version |
Description: Define the power function on complex numbers. Because df-relog 13118 is only defined on positive reals, this definition only allows for a base which is a positive real. (Contributed by Jim Kingdon, 12-Jun-2024.) |
Ref | Expression |
---|---|
df-rpcxp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccxp 13117 |
. 2
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2 | vx |
. . 3
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3 | vy |
. . 3
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4 | crp 9538 |
. . 3
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5 | cc 7709 |
. . 3
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6 | 3 | cv 1331 |
. . . . 5
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7 | 2 | cv 1331 |
. . . . . 6
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8 | clog 13116 |
. . . . . 6
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9 | 7, 8 | cfv 5163 |
. . . . 5
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10 | cmul 7716 |
. . . . 5
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11 | 6, 9, 10 | co 5814 |
. . . 4
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12 | ce 11516 |
. . . 4
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13 | 11, 12 | cfv 5163 |
. . 3
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14 | 2, 3, 4, 5, 13 | cmpo 5816 |
. 2
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15 | 1, 14 | wceq 1332 |
1
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Colors of variables: wff set class |
This definition is referenced by: rpcxpef 13154 |
Copyright terms: Public domain | W3C validator |