Description: The span of a basis is the whole space. (Contributed by Mario Carneiro, 24-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lbsss.v | |
|
lbsss.j | |
||
lbssp.n | |
||
Assertion | lbssp | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lbsss.v | |
|
2 | lbsss.j | |
|
3 | lbssp.n | |
|
4 | elfvdm | |
|
5 | 4 2 | eleq2s | |
6 | eqid | |
|
7 | eqid | |
|
8 | eqid | |
|
9 | eqid | |
|
10 | 1 6 7 8 2 3 9 | islbs | |
11 | 5 10 | syl | |
12 | 11 | ibi | |
13 | 12 | simp2d | |