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Mirrors > Home > ILE Home > Th. List > ax-mulrcl | Unicode version |
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 7554. Proofs should normally use remulcl 7620 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulrcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cr 7499 |
. . . 4
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3 | 1, 2 | wcel 1448 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 1448 |
. . 3
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6 | 3, 5 | wa 103 |
. 2
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7 | cmul 7505 |
. . . 4
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8 | 1, 4, 7 | co 5706 |
. . 3
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9 | 8, 2 | wcel 1448 |
. 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: remulcl 7620 |
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