Description: A vector X which doesn't belong to a subspace U is nonzero. (Contributed by NM, 14-May-2015) (Revised by AV, 17-Jul-2022) (Proof shortened by AV, 19-Jul-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lssneln0.o | |
|
lssneln0.s | |
||
lssneln0.w | |
||
lssneln0.u | |
||
lssneln0.x | |
||
lssneln0.n | |
||
Assertion | lssneln0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lssneln0.o | |
|
2 | lssneln0.s | |
|
3 | lssneln0.w | |
|
4 | lssneln0.u | |
|
5 | lssneln0.x | |
|
6 | lssneln0.n | |
|
7 | 1 2 3 4 6 | lssvneln0 | |
8 | eldifsn | |
|
9 | 5 7 8 | sylanbrc | |