Description: Cancellation law for vector addition. (Contributed by NM, 11-Sep-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hvnegdi.1 | |
|
hvnegdi.2 | |
||
hvaddcan.3 | |
||
Assertion | hvaddcani | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hvnegdi.1 | |
|
2 | hvnegdi.2 | |
|
3 | hvaddcan.3 | |
|
4 | oveq1 | |
|
5 | neg1cn | |
|
6 | 5 1 | hvmulcli | |
7 | 1 2 6 | hvadd32i | |
8 | 1 | hvnegidi | |
9 | 8 | oveq1i | |
10 | 2 | hvaddlidi | |
11 | 7 9 10 | 3eqtri | |
12 | 1 3 6 | hvadd32i | |
13 | 8 | oveq1i | |
14 | 3 | hvaddlidi | |
15 | 12 13 14 | 3eqtri | |
16 | 4 11 15 | 3eqtr3g | |
17 | oveq2 | |
|
18 | 16 17 | impbii | |