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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 7889. Proofs should normally use mulass 7959 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 7826 |
. . . 4
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3 | 1, 2 | wcel 2159 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 2159 |
. . 3
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6 | cC |
. . . 4
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7 | 6, 2 | wcel 2159 |
. . 3
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8 | 3, 5, 7 | w3a 979 |
. 2
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9 | cmul 7833 |
. . . . 5
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10 | 1, 4, 9 | co 5890 |
. . . 4
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11 | 10, 6, 9 | co 5890 |
. . 3
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12 | 4, 6, 9 | co 5890 |
. . . 4
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13 | 1, 12, 9 | co 5890 |
. . 3
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14 | 11, 13 | wceq 1363 |
. 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 7959 |
Copyright terms: Public domain | W3C validator |