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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 7864. Proofs should normally use mulcl 7937 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 7808 |
. . . 4
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3 | 1, 2 | wcel 2148 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 2148 |
. . 3
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6 | 3, 5 | wa 104 |
. 2
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7 | cmul 7815 |
. . . 4
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8 | 1, 4, 7 | co 5874 |
. . 3
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9 | 8, 2 | wcel 2148 |
. 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 7937 |
Copyright terms: Public domain | W3C validator |