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Mirrors > Home > MPE Home > Th. List > ax-mulcom | Structured version Visualization version Unicode version |
Description: Multiplication of complex numbers is commutative. Axiom 8 of 22 for real and complex numbers, justified by theorem axmulcom 9597. Proofs should normally use mulcom 9643 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulcom |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
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2 | cc 9555 |
. . . 4
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3 | 1, 2 | wcel 1904 |
. . 3
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4 | cB |
. . . 4
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5 | 4, 2 | wcel 1904 |
. . 3
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6 | 3, 5 | wa 376 |
. 2
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7 | cmul 9562 |
. . . 4
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8 | 1, 4, 7 | co 6308 |
. . 3
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9 | 4, 1, 7 | co 6308 |
. . 3
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10 | 8, 9 | wceq 1452 |
. 2
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11 | 6, 10 | wi 4 |
1
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Colors of variables: wff setvar class |
This axiom is referenced by: mulcom 9643 |
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