Description: Order preservation of the one-to-one onto mapping between the two sublattices in Lemma 1.3 of MaedaMaeda p. 2. (Contributed by NM, 27-Apr-2006) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mdslle1.1 | |
|
mdslle1.2 | |
||
mdslle1.3 | |
||
mdslle1.4 | |
||
Assertion | mdslle1i | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mdslle1.1 | |
|
2 | mdslle1.2 | |
|
3 | mdslle1.3 | |
|
4 | mdslle1.4 | |
|
5 | ssrin | |
|
6 | 3 2 | chincli | |
7 | 4 2 | chincli | |
8 | 6 7 1 | chlej1i | |
9 | id | |
|
10 | ssin | |
|
11 | 10 | bicomi | |
12 | 11 | simplbi | |
13 | 1 2 | chjcli | |
14 | 3 4 13 | chlubi | |
15 | 14 | bicomi | |
16 | 15 | simplbi | |
17 | 1 2 3 | 3pm3.2i | |
18 | dmdsl3 | |
|
19 | 17 18 | mpan | |
20 | 9 12 16 19 | syl3an | |
21 | 11 | simprbi | |
22 | 15 | simprbi | |
23 | 1 2 4 | 3pm3.2i | |
24 | dmdsl3 | |
|
25 | 23 24 | mpan | |
26 | 9 21 22 25 | syl3an | |
27 | 20 26 | sseq12d | |
28 | 8 27 | syl5ib | |
29 | 5 28 | impbid2 | |