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Mirrors > Home > MPE Home > Th. List > ax-distr | Unicode version |
Description: Distributive law for complex numbers (left-distributivity). Axiom 11 of 22 for real and complex numbers, justified by theorem axdistr 9556. Proofs should normally use adddi 9602 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-distr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cc 9511 | . . . 4 | |
3 | 1, 2 | wcel 1818 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1818 | . . 3 |
6 | cC | . . . 4 | |
7 | 6, 2 | wcel 1818 | . . 3 |
8 | 3, 5, 7 | w3a 973 | . 2 |
9 | caddc 9516 | . . . . 5 | |
10 | 4, 6, 9 | co 6296 | . . . 4 |
11 | cmul 9518 | . . . 4 | |
12 | 1, 10, 11 | co 6296 | . . 3 |
13 | 1, 4, 11 | co 6296 | . . . 4 |
14 | 1, 6, 11 | co 6296 | . . . 4 |
15 | 13, 14, 9 | co 6296 | . . 3 |
16 | 12, 15 | wceq 1395 | . 2 |
17 | 8, 16 | wi 4 | 1 |
Colors of variables: wff setvar class |
This axiom is referenced by: adddi 9602 |
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