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Mirrors > Home > ILE Home > Th. List > ax-addass | Unicode version |
Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 7900. Proofs should normally use addass 7970 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-addass |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cc 7838 |
. . . 4
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3 | 1, 2 | wcel 2160 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 2160 |
. . 3
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6 | cC |
. . . 4
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7 | 6, 2 | wcel 2160 |
. . 3
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8 | 3, 5, 7 | w3a 980 |
. 2
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9 | caddc 7843 |
. . . . 5
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10 | 1, 4, 9 | co 5895 |
. . . 4
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11 | 10, 6, 9 | co 5895 |
. . 3
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12 | 4, 6, 9 | co 5895 |
. . . 4
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13 | 1, 12, 9 | co 5895 |
. . 3
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14 | 11, 13 | wceq 1364 |
. 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: addass 7970 |
Copyright terms: Public domain | W3C validator |