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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 7166. Proofs should normally use mulcl 7232 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 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 | 3, 5 | wa 102 |
. 2
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7 | cmul 7118 |
. . . 4
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8 | 1, 4, 7 | co 5564 |
. . 3
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9 | 8, 2 | wcel 1434 |
. 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 7232 |
Copyright terms: Public domain | W3C validator |