Step |
Hyp |
Ref |
Expression |
1 |
|
lshpdisj.v |
|
2 |
|
lshpdisj.o |
|
3 |
|
lshpdisj.n |
|
4 |
|
lshpdisj.p |
|
5 |
|
lshpdisj.h |
|
6 |
|
lshpdisj.w |
|
7 |
|
lshpdisj.u |
|
8 |
|
lshpdisj.x |
|
9 |
|
lshpdisj.e |
|
10 |
|
lveclmod |
|
11 |
6 10
|
syl |
|
12 |
11
|
adantr |
|
13 |
8
|
adantr |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
|
eqid |
|
17 |
14 15 1 16 3
|
lspsnel |
|
18 |
12 13 17
|
syl2anc |
|
19 |
1 3 4 5 11 7 8 9
|
lshpnel |
|
20 |
19
|
ad2antrr |
|
21 |
|
eqid |
|
22 |
6
|
ad2antrr |
|
23 |
21 5 11 7
|
lshplss |
|
24 |
23
|
ad2antrr |
|
25 |
8
|
ad2antrr |
|
26 |
11
|
adantr |
|
27 |
|
simpr |
|
28 |
8
|
adantr |
|
29 |
1 16 14 15 3 26 27 28
|
lspsneli |
|
30 |
29
|
adantr |
|
31 |
|
simpr |
|
32 |
1 2 21 3 22 24 25 30 31
|
lspsnel4 |
|
33 |
20 32
|
mtbid |
|
34 |
33
|
ex |
|
35 |
34
|
necon4ad |
|
36 |
|
eleq1 |
|
37 |
|
eqeq1 |
|
38 |
36 37
|
imbi12d |
|
39 |
35 38
|
syl5ibrcom |
|
40 |
39
|
ex |
|
41 |
40
|
com23 |
|
42 |
41
|
com24 |
|
43 |
42
|
imp31 |
|
44 |
43
|
rexlimdva |
|
45 |
18 44
|
sylbid |
|
46 |
45
|
expimpd |
|
47 |
|
elin |
|
48 |
|
velsn |
|
49 |
46 47 48
|
3imtr4g |
|
50 |
49
|
ssrdv |
|
51 |
1 21 3
|
lspsncl |
|
52 |
11 8 51
|
syl2anc |
|
53 |
21
|
lssincl |
|
54 |
11 23 52 53
|
syl3anc |
|
55 |
2 21
|
lss0ss |
|
56 |
11 54 55
|
syl2anc |
|
57 |
50 56
|
eqssd |
|