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Mirrors > Home > ILE Home > Th. List > ax-mulcl | Unicode version |
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 6752. Proofs should normally use mulcl 6806 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cc 6709 |
. . . 4
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3 | 1, 2 | wcel 1390 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 1390 |
. . 3
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6 | 3, 5 | wa 97 |
. 2
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7 | cmul 6716 |
. . . 4
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8 | 1, 4, 7 | co 5455 |
. . 3
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9 | 8, 2 | wcel 1390 |
. 2
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10 | 6, 9 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: mulcl 6806 |
Copyright terms: Public domain | W3C validator |