Step |
Hyp |
Ref |
Expression |
1 |
|
lshpnel2.v |
|
2 |
|
lshpnel2.s |
|
3 |
|
lshpnel2.n |
|
4 |
|
lshpnel2.p |
|
5 |
|
lshpnel2.h |
|
6 |
|
lshpnel2.w |
|
7 |
|
lshpnel2.u |
|
8 |
|
lshpnel2.t |
|
9 |
|
lshpnel2.x |
|
10 |
|
lshpnel2.e |
|
11 |
10
|
adantr |
|
12 |
6
|
adantr |
|
13 |
|
simpr |
|
14 |
9
|
adantr |
|
15 |
1 3 4 5 12 13 14
|
lshpnelb |
|
16 |
11 15
|
mpbid |
|
17 |
7
|
adantr |
|
18 |
8
|
adantr |
|
19 |
9
|
adantr |
|
20 |
|
lveclmod |
|
21 |
6 20
|
syl |
|
22 |
2 3
|
lspid |
|
23 |
21 7 22
|
syl2anc |
|
24 |
23
|
uneq1d |
|
25 |
24
|
fveq2d |
|
26 |
1 2
|
lssss |
|
27 |
7 26
|
syl |
|
28 |
9
|
snssd |
|
29 |
1 3
|
lspun |
|
30 |
21 27 28 29
|
syl3anc |
|
31 |
1 2 3
|
lspsncl |
|
32 |
21 9 31
|
syl2anc |
|
33 |
2 3 4
|
lsmsp |
|
34 |
21 7 32 33
|
syl3anc |
|
35 |
25 30 34
|
3eqtr4rd |
|
36 |
35
|
eqeq1d |
|
37 |
36
|
biimpa |
|
38 |
|
sneq |
|
39 |
38
|
uneq2d |
|
40 |
39
|
fveqeq2d |
|
41 |
40
|
rspcev |
|
42 |
19 37 41
|
syl2anc |
|
43 |
6
|
adantr |
|
44 |
1 3 2 5
|
islshp |
|
45 |
43 44
|
syl |
|
46 |
17 18 42 45
|
mpbir3and |
|
47 |
16 46
|
impbida |
|