Description: Hilbert vector space addition law. (Contributed by NM, 31-Oct-1999) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hvass.1 | |
|
hvass.2 | |
||
hvass.3 | |
||
hvadd4.4 | |
||
Assertion | hvsubsub4i | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hvass.1 | |
|
2 | hvass.2 | |
|
3 | hvass.3 | |
|
4 | hvadd4.4 | |
|
5 | neg1cn | |
|
6 | 5 2 | hvmulcli | |
7 | 5 3 | hvmulcli | |
8 | 5 4 | hvmulcli | |
9 | 5 8 | hvmulcli | |
10 | 1 6 7 9 | hvadd4i | |
11 | 5 3 8 | hvdistr1i | |
12 | 11 | oveq2i | |
13 | 5 2 8 | hvdistr1i | |
14 | 13 | oveq2i | |
15 | 10 12 14 | 3eqtr4i | |
16 | 1 6 | hvaddcli | |
17 | 3 8 | hvaddcli | |
18 | 16 17 | hvsubvali | |
19 | 1 7 | hvaddcli | |
20 | 2 8 | hvaddcli | |
21 | 19 20 | hvsubvali | |
22 | 15 18 21 | 3eqtr4i | |
23 | 1 2 | hvsubvali | |
24 | 3 4 | hvsubvali | |
25 | 23 24 | oveq12i | |
26 | 1 3 | hvsubvali | |
27 | 2 4 | hvsubvali | |
28 | 26 27 | oveq12i | |
29 | 22 25 28 | 3eqtr4i | |