Description: Lattice meet is idempotent. Analogue of inidm . (Contributed by NM, 8-Nov-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | latmidm.b | |
|
latmidm.m | |
||
Assertion | latmidm | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | latmidm.b | |
|
2 | latmidm.m | |
|
3 | eqid | |
|
4 | simpl | |
|
5 | 1 2 | latmcl | |
6 | 5 | 3anidm23 | |
7 | simpr | |
|
8 | 1 3 2 | latmle1 | |
9 | 8 | 3anidm23 | |
10 | 1 3 | latref | |
11 | 1 3 2 | latlem12 | |
12 | 4 7 7 7 11 | syl13anc | |
13 | 10 10 12 | mpbi2and | |
14 | 1 3 4 6 7 9 13 | latasymd | |