Step |
Hyp |
Ref |
Expression |
1 |
|
pl42lem.b |
|
2 |
|
pl42lem.l |
|
3 |
|
pl42lem.j |
|
4 |
|
pl42lem.m |
|
5 |
|
pl42lem.o |
|
6 |
|
pl42lem.f |
|
7 |
|
pl42lem.p |
|
8 |
|
simp11 |
|
9 |
8
|
hllatd |
|
10 |
|
simp12 |
|
11 |
|
simp13 |
|
12 |
1 3
|
latjcl |
|
13 |
9 10 11 12
|
syl3anc |
|
14 |
|
simp21 |
|
15 |
1 4
|
latmcl |
|
16 |
9 13 14 15
|
syl3anc |
|
17 |
|
simp22 |
|
18 |
1 3
|
latjcl |
|
19 |
9 16 17 18
|
syl3anc |
|
20 |
|
simp23 |
|
21 |
|
eqid |
|
22 |
1 4 21 6
|
pmapmeet |
|
23 |
8 19 20 22
|
syl3anc |
|
24 |
|
hlop |
|
25 |
8 24
|
syl |
|
26 |
1 5
|
opoccl |
|
27 |
25 17 26
|
syl2anc |
|
28 |
1 2 4
|
latmle2 |
|
29 |
9 13 14 28
|
syl3anc |
|
30 |
|
simp3r |
|
31 |
1 2 9 16 14 27 29 30
|
lattrd |
|
32 |
1 2 3 6 5 7
|
pmapojoinN |
|
33 |
8 16 17 31 32
|
syl31anc |
|
34 |
1 4 21 6
|
pmapmeet |
|
35 |
8 13 14 34
|
syl3anc |
|
36 |
|
simp3l |
|
37 |
1 2 3 6 5 7
|
pmapojoinN |
|
38 |
8 10 11 36 37
|
syl31anc |
|
39 |
38
|
ineq1d |
|
40 |
35 39
|
eqtrd |
|
41 |
40
|
oveq1d |
|
42 |
33 41
|
eqtrd |
|
43 |
42
|
ineq1d |
|
44 |
23 43
|
eqtrd |
|
45 |
44
|
3expia |
|