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| Description: Scalar multiplication distributive law. |
| Ref | Expression |
|---|---|
| ax-hvdistr2 |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cA |
. . . 4
| |
| 2 | cc 6384 |
. . . 4
| |
| 3 | 1, 2 | wcel 1300 |
. . 3
|
| 4 | cB |
. . . 4
| |
| 5 | 4, 2 | wcel 1300 |
. . 3
|
| 6 | cC |
. . . 4
| |
| 7 | chil 10420 |
. . . 4
| |
| 8 | 6, 7 | wcel 1300 |
. . 3
|
| 9 | 3, 5, 8 | w3a 858 |
. 2
|
| 10 | caddc 6389 |
. . . . 5
| |
| 11 | 1, 4, 10 | co 4884 |
. . . 4
|
| 12 | csm 10422 |
. . . 4
| |
| 13 | 11, 6, 12 | co 4884 |
. . 3
|
| 14 | 1, 6, 12 | co 4884 |
. . . 4
|
| 15 | 4, 6, 12 | co 4884 |
. . . 4
|
| 16 | cva 10421 |
. . . 4
| |
| 17 | 14, 15, 16 | co 4884 |
. . 3
|
| 18 | 13, 17 | wceq 1298 |
. 2
|
| 19 | 9, 18 | wi 3 |
1
|
| Colors of variables: wff set class |
| This axiom is referenced by: hvsubid 10527 hvsubdistr2 10549 hv2times 10560 hilvc 10662 hhssnv 10767 hoadddir 11367 superpos 11926 |