Description: Meet with lattice zero is zero. (Contributed by NM, 9-Oct-2012)
Ref | Expression | ||
---|---|---|---|
Hypotheses | olm0.b | |
|
olm0.m | |
||
olm0.z | |
||
Assertion | olm02 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olm0.b | |
|
2 | olm0.m | |
|
3 | olm0.z | |
|
4 | ollat | |
|
5 | 4 | adantr | |
6 | simpr | |
|
7 | olop | |
|
8 | 7 | adantr | |
9 | 1 3 | op0cl | |
10 | 8 9 | syl | |
11 | 1 2 | latmcom | |
12 | 5 6 10 11 | syl3anc | |
13 | 1 2 3 | olm01 | |
14 | 12 13 | eqtr3d | |