Step |
Hyp |
Ref |
Expression |
1 |
|
lshpset2.v |
|
2 |
|
lshpset2.d |
|
3 |
|
lshpset2.z |
|
4 |
|
lshpset2.h |
|
5 |
|
lshpset2.f |
|
6 |
|
lshpset2.k |
|
7 |
4 5 6
|
lshpkrex |
|
8 |
|
eleq1 |
|
9 |
8
|
biimparc |
|
10 |
9
|
adantll |
|
11 |
10
|
adantlr |
|
12 |
|
simplll |
|
13 |
|
simplr |
|
14 |
1 2 3 4 5 6 12 13
|
lkrshp3 |
|
15 |
11 14
|
mpbid |
|
16 |
15
|
ex |
|
17 |
|
eqimss2 |
|
18 |
|
eqimss |
|
19 |
17 18
|
eqssd |
|
20 |
19
|
a1i |
|
21 |
16 20
|
jcad |
|
22 |
21
|
reximdva |
|
23 |
7 22
|
mpd |
|
24 |
23
|
ex |
|
25 |
1 2 3 4 5 6
|
lkrshp |
|
26 |
25
|
3adant3r |
|
27 |
|
eqid |
|
28 |
|
eqid |
|
29 |
1 27 28 4
|
islshp |
|
30 |
29
|
3ad2ant1 |
|
31 |
26 30
|
mpbid |
|
32 |
|
eleq1 |
|
33 |
|
neeq1 |
|
34 |
|
uneq1 |
|
35 |
34
|
fveqeq2d |
|
36 |
35
|
rexbidv |
|
37 |
32 33 36
|
3anbi123d |
|
38 |
37
|
adantl |
|
39 |
38
|
3ad2ant3 |
|
40 |
31 39
|
mpbird |
|
41 |
40
|
rexlimdv3a |
|
42 |
1 27 28 4
|
islshp |
|
43 |
41 42
|
sylibrd |
|
44 |
24 43
|
impbid |
|
45 |
44
|
abbi2dv |
|