Step |
Hyp |
Ref |
Expression |
1 |
|
lhpmod.b |
|
2 |
|
lhpmod.l |
|
3 |
|
lhpmod.j |
|
4 |
|
lhpmod.m |
|
5 |
|
lhpmod.h |
|
6 |
|
simp1l |
|
7 |
|
simp1r |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
8 9 5
|
lhpocat |
|
11 |
6 7 10
|
syl2anc |
|
12 |
|
hlop |
|
13 |
6 12
|
syl |
|
14 |
|
simp2l |
|
15 |
1 8
|
opoccl |
|
16 |
13 14 15
|
syl2anc |
|
17 |
|
simp2r |
|
18 |
1 8
|
opoccl |
|
19 |
13 17 18
|
syl2anc |
|
20 |
|
simp3 |
|
21 |
1 2 8
|
oplecon3b |
|
22 |
13 17 14 21
|
syl3anc |
|
23 |
20 22
|
mpbid |
|
24 |
1 2 3 4 9
|
atmod1i2 |
|
25 |
6 11 16 19 23 24
|
syl131anc |
|
26 |
6
|
hllatd |
|
27 |
1 5
|
lhpbase |
|
28 |
7 27
|
syl |
|
29 |
1 4
|
latmcl |
|
30 |
26 14 28 29
|
syl3anc |
|
31 |
1 3
|
latjcl |
|
32 |
26 30 17 31
|
syl3anc |
|
33 |
1 3
|
latjcl |
|
34 |
26 28 17 33
|
syl3anc |
|
35 |
1 4
|
latmcl |
|
36 |
26 14 34 35
|
syl3anc |
|
37 |
1 8
|
opcon3b |
|
38 |
13 32 36 37
|
syl3anc |
|
39 |
|
hlol |
|
40 |
6 39
|
syl |
|
41 |
1 3 4 8
|
oldmm1 |
|
42 |
40 14 34 41
|
syl3anc |
|
43 |
1 3 4 8
|
oldmj1 |
|
44 |
40 28 17 43
|
syl3anc |
|
45 |
44
|
oveq2d |
|
46 |
42 45
|
eqtrd |
|
47 |
1 3 4 8
|
oldmj1 |
|
48 |
40 30 17 47
|
syl3anc |
|
49 |
1 3 4 8
|
oldmm1 |
|
50 |
40 14 28 49
|
syl3anc |
|
51 |
50
|
oveq1d |
|
52 |
48 51
|
eqtrd |
|
53 |
46 52
|
eqeq12d |
|
54 |
38 53
|
bitrd |
|
55 |
25 54
|
mpbird |
|