Description: A basis has no proper subsets that are also bases. (Contributed by Mario Carneiro, 23-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | obs2ss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 | |
|
2 | eqid | |
|
3 | 2 | obsne0 | |
4 | 3 | 3ad2antl1 | |
5 | eqid | |
|
6 | 5 | obselocv | |
7 | 6 | 3expa | |
8 | 7 | 3adantl2 | |
9 | simpl2 | |
|
10 | 2 5 | obsocv | |
11 | 9 10 | syl | |
12 | 11 | eleq2d | |
13 | elsni | |
|
14 | 12 13 | syl6bi | |
15 | 8 14 | sylbird | |
16 | 15 | necon1ad | |
17 | 4 16 | mpd | |
18 | 1 17 | eqelssd | |