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Mirrors > Home > ILE Home > Th. List > ax-mulass | Unicode version |
Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7311. Proofs should normally use mulass 7376 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cc 7251 |
. . . 4
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3 | 1, 2 | wcel 1434 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 1434 |
. . 3
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6 | cC |
. . . 4
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7 | 6, 2 | wcel 1434 |
. . 3
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8 | 3, 5, 7 | w3a 920 |
. 2
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9 | cmul 7258 |
. . . . 5
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10 | 1, 4, 9 | co 5591 |
. . . 4
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11 | 10, 6, 9 | co 5591 |
. . 3
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12 | 4, 6, 9 | co 5591 |
. . . 4
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13 | 1, 12, 9 | co 5591 |
. . 3
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14 | 11, 13 | wceq 1285 |
. 2
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15 | 8, 14 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: mulass 7376 |
Copyright terms: Public domain | W3C validator |