Step |
Hyp |
Ref |
Expression |
1 |
|
lhpocnle.l |
|
2 |
|
lhpocnle.o |
|
3 |
|
lhpocnle.h |
|
4 |
|
hlatl |
|
5 |
4
|
adantr |
|
6 |
|
simpr |
|
7 |
|
eqid |
|
8 |
7 3
|
lhpbase |
|
9 |
|
eqid |
|
10 |
7 2 9 3
|
lhpoc |
|
11 |
8 10
|
sylan2 |
|
12 |
6 11
|
mpbid |
|
13 |
|
eqid |
|
14 |
13 9
|
atn0 |
|
15 |
5 12 14
|
syl2anc |
|
16 |
15
|
neneqd |
|
17 |
|
simpr |
|
18 |
|
hllat |
|
19 |
18
|
ad2antrr |
|
20 |
|
hlop |
|
21 |
20
|
ad2antrr |
|
22 |
8
|
ad2antlr |
|
23 |
7 2
|
opoccl |
|
24 |
21 22 23
|
syl2anc |
|
25 |
7 1
|
latref |
|
26 |
19 24 25
|
syl2anc |
|
27 |
|
eqid |
|
28 |
7 1 27
|
latlem12 |
|
29 |
19 24 22 24 28
|
syl13anc |
|
30 |
17 26 29
|
mpbi2and |
|
31 |
7 2 27 13
|
opnoncon |
|
32 |
21 22 31
|
syl2anc |
|
33 |
30 32
|
breqtrd |
|
34 |
7 1 13
|
ople0 |
|
35 |
21 24 34
|
syl2anc |
|
36 |
33 35
|
mpbid |
|
37 |
16 36
|
mtand |
|