Description: Additive property of a linear Hilbert space functional. (Contributed by NM, 11-Feb-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | lnfnl.1 | |
|
Assertion | lnfnaddi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lnfnl.1 | |
|
2 | ax-1cn | |
|
3 | 1 | lnfnli | |
4 | 2 3 | mp3an1 | |
5 | ax-hvmulid | |
|
6 | 5 | fvoveq1d | |
7 | 6 | adantr | |
8 | 1 | lnfnfi | |
9 | 8 | ffvelrni | |
10 | 9 | mulid2d | |
11 | 10 | adantr | |
12 | 11 | oveq1d | |
13 | 4 7 12 | 3eqtr3d | |