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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 7170. Proofs should normally use addass 7235 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 7111 |
. . . 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 | caddc 7116 |
. . . . 5
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10 | 1, 4, 9 | co 5564 |
. . . 4
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11 | 10, 6, 9 | co 5564 |
. . 3
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12 | 4, 6, 9 | co 5564 |
. . . 4
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13 | 1, 12, 9 | co 5564 |
. . 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: addass 7235 |
Copyright terms: Public domain | W3C validator |