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Mirrors > Home > ILE Home > Th. List > ax-distr | Unicode version |
Description: Distributive law for complex numbers (left-distributivity). Axiom for real and complex numbers, justified by Theorem axdistr 7861. Proofs should normally use adddi 7931 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-distr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cc 7797 |
. . . 4
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3 | 1, 2 | wcel 2148 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 2148 |
. . 3
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6 | cC |
. . . 4
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7 | 6, 2 | wcel 2148 |
. . 3
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8 | 3, 5, 7 | w3a 978 |
. 2
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9 | caddc 7802 |
. . . . 5
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10 | 4, 6, 9 | co 5869 |
. . . 4
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11 | cmul 7804 |
. . . 4
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12 | 1, 10, 11 | co 5869 |
. . 3
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13 | 1, 4, 11 | co 5869 |
. . . 4
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14 | 1, 6, 11 | co 5869 |
. . . 4
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15 | 13, 14, 9 | co 5869 |
. . 3
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16 | 12, 15 | wceq 1353 |
. 2
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17 | 8, 16 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: adddi 7931 |
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