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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 7307. Proofs should normally use remulcl 7373 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 7252 |
. . . 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 7258 |
. . . 4
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8 | 1, 4, 7 | co 5591 |
. . 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: remulcl 7373 |
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