Description: The kernel of a nonzero scalar product of a functional equals the kernel of the functional. (Contributed by NM, 28-Dec-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ldualkrsc.r | |
|
ldualkrsc.k | |
||
ldualkrsc.o | |
||
ldualkrsc.f | |
||
ldualkrsc.l | |
||
ldualkrsc.d | |
||
ldualkrsc.s | |
||
ldualkrsc.w | |
||
ldualkrsc.g | |
||
ldualkrsc.x | |
||
ldualkrsc.e | |
||
Assertion | ldualkrsc | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ldualkrsc.r | |
|
2 | ldualkrsc.k | |
|
3 | ldualkrsc.o | |
|
4 | ldualkrsc.f | |
|
5 | ldualkrsc.l | |
|
6 | ldualkrsc.d | |
|
7 | ldualkrsc.s | |
|
8 | ldualkrsc.w | |
|
9 | ldualkrsc.g | |
|
10 | ldualkrsc.x | |
|
11 | ldualkrsc.e | |
|
12 | eqid | |
|
13 | eqid | |
|
14 | 4 12 1 2 13 6 7 8 10 9 | ldualvs | |
15 | 14 | fveq2d | |
16 | 12 1 2 13 4 5 8 9 10 3 11 | lkrsc | |
17 | 15 16 | eqtrd | |