Step |
Hyp |
Ref |
Expression |
1 |
|
pmapj2.b |
|
2 |
|
pmapj2.j |
|
3 |
|
pmapj2.m |
|
4 |
|
pmapj2.p |
|
5 |
|
pmapj2.o |
|
6 |
|
simp1 |
|
7 |
|
hllat |
|
8 |
7
|
3ad2ant1 |
|
9 |
|
hlop |
|
10 |
9
|
3ad2ant1 |
|
11 |
|
simp2 |
|
12 |
|
eqid |
|
13 |
1 12
|
opoccl |
|
14 |
10 11 13
|
syl2anc |
|
15 |
|
simp3 |
|
16 |
1 12
|
opoccl |
|
17 |
10 15 16
|
syl2anc |
|
18 |
|
eqid |
|
19 |
1 18
|
latmcl |
|
20 |
8 14 17 19
|
syl3anc |
|
21 |
1 12 3 5
|
polpmapN |
|
22 |
6 20 21
|
syl2anc |
|
23 |
1 12 3 5
|
polpmapN |
|
24 |
23
|
3adant3 |
|
25 |
1 12 3 5
|
polpmapN |
|
26 |
25
|
3adant2 |
|
27 |
24 26
|
ineq12d |
|
28 |
|
eqid |
|
29 |
1 28 3
|
pmapssat |
|
30 |
29
|
3adant3 |
|
31 |
1 28 3
|
pmapssat |
|
32 |
31
|
3adant2 |
|
33 |
28 4 5
|
poldmj1N |
|
34 |
6 30 32 33
|
syl3anc |
|
35 |
1 18 28 3
|
pmapmeet |
|
36 |
6 14 17 35
|
syl3anc |
|
37 |
27 34 36
|
3eqtr4rd |
|
38 |
37
|
fveq2d |
|
39 |
|
hlol |
|
40 |
1 2 18 12
|
oldmm4 |
|
41 |
39 40
|
syl3an1 |
|
42 |
41
|
fveq2d |
|
43 |
22 38 42
|
3eqtr3rd |
|