Step |
Hyp |
Ref |
Expression |
1 |
|
lhprelat3.b |
|
2 |
|
lhprelat3.l |
|
3 |
|
lhprelat3.s |
|
4 |
|
lhprelat3.m |
|
5 |
|
lhprelat3.c |
|
6 |
|
lhprelat3.h |
|
7 |
|
simpr |
|
8 |
|
simpll1 |
|
9 |
|
eqid |
|
10 |
1 9
|
atbase |
|
11 |
10
|
adantl |
|
12 |
|
eqid |
|
13 |
1 12 9 6
|
lhpoc2N |
|
14 |
8 11 13
|
syl2anc |
|
15 |
7 14
|
mpbid |
|
16 |
15
|
adantr |
|
17 |
|
hlop |
|
18 |
8 17
|
syl |
|
19 |
8
|
hllatd |
|
20 |
|
simpll3 |
|
21 |
1 12
|
opoccl |
|
22 |
18 11 21
|
syl2anc |
|
23 |
1 4
|
latmcl |
|
24 |
19 20 22 23
|
syl3anc |
|
25 |
1 12 5
|
cvrcon3b |
|
26 |
18 24 20 25
|
syl3anc |
|
27 |
|
hlol |
|
28 |
8 27
|
syl |
|
29 |
|
eqid |
|
30 |
1 29 4 12
|
oldmm3N |
|
31 |
28 20 11 30
|
syl3anc |
|
32 |
31
|
breq2d |
|
33 |
26 32
|
bitr2d |
|
34 |
|
simpll2 |
|
35 |
1 2 12
|
oplecon3b |
|
36 |
18 34 24 35
|
syl3anc |
|
37 |
31
|
breq1d |
|
38 |
36 37
|
bitr2d |
|
39 |
33 38
|
anbi12d |
|
40 |
39
|
biimpa |
|
41 |
40
|
ancomd |
|
42 |
|
oveq2 |
|
43 |
42
|
breq2d |
|
44 |
42
|
breq1d |
|
45 |
43 44
|
anbi12d |
|
46 |
45
|
rspcev |
|
47 |
16 41 46
|
syl2anc |
|
48 |
|
simpl1 |
|
49 |
48 17
|
syl |
|
50 |
|
simpl3 |
|
51 |
1 12
|
opoccl |
|
52 |
49 50 51
|
syl2anc |
|
53 |
|
simpl2 |
|
54 |
1 12
|
opoccl |
|
55 |
49 53 54
|
syl2anc |
|
56 |
|
simpr |
|
57 |
1 3 12
|
opltcon3b |
|
58 |
49 53 50 57
|
syl3anc |
|
59 |
56 58
|
mpbid |
|
60 |
1 2 3 29 5 9
|
hlrelat3 |
|
61 |
48 52 55 59 60
|
syl31anc |
|
62 |
47 61
|
r19.29a |
|