Step |
Hyp |
Ref |
Expression |
1 |
|
lplni2.l |
|
2 |
|
lplni2.j |
|
3 |
|
lplni2.a |
|
4 |
|
lplni2.p |
|
5 |
|
simp2 |
|
6 |
|
simp3l |
|
7 |
|
simp3r |
|
8 |
|
eqidd |
|
9 |
|
neeq1 |
|
10 |
|
oveq1 |
|
11 |
10
|
breq2d |
|
12 |
11
|
notbid |
|
13 |
10
|
oveq1d |
|
14 |
13
|
eqeq2d |
|
15 |
9 12 14
|
3anbi123d |
|
16 |
|
neeq2 |
|
17 |
|
oveq2 |
|
18 |
17
|
breq2d |
|
19 |
18
|
notbid |
|
20 |
17
|
oveq1d |
|
21 |
20
|
eqeq2d |
|
22 |
16 19 21
|
3anbi123d |
|
23 |
|
breq1 |
|
24 |
23
|
notbid |
|
25 |
|
oveq2 |
|
26 |
25
|
eqeq2d |
|
27 |
24 26
|
3anbi23d |
|
28 |
15 22 27
|
rspc3ev |
|
29 |
5 6 7 8 28
|
syl13anc |
|
30 |
|
simp1 |
|
31 |
|
hllat |
|
32 |
31
|
3ad2ant1 |
|
33 |
|
simp21 |
|
34 |
|
simp22 |
|
35 |
|
eqid |
|
36 |
35 2 3
|
hlatjcl |
|
37 |
30 33 34 36
|
syl3anc |
|
38 |
|
simp23 |
|
39 |
35 3
|
atbase |
|
40 |
38 39
|
syl |
|
41 |
35 2
|
latjcl |
|
42 |
32 37 40 41
|
syl3anc |
|
43 |
35 1 2 3 4
|
islpln5 |
|
44 |
30 42 43
|
syl2anc |
|
45 |
29 44
|
mpbird |
|