Step |
Hyp |
Ref |
Expression |
1 |
|
lsatcvat.o |
|
2 |
|
lsatcvat.s |
|
3 |
|
lsatcvat.p |
|
4 |
|
lsatcvat.a |
|
5 |
|
lsatcvat.w |
|
6 |
|
lsatcvat.u |
|
7 |
|
lsatcvat.q |
|
8 |
|
lsatcvat.r |
|
9 |
|
lsatcvat.n |
|
10 |
|
lsatcvat.l |
|
11 |
5
|
adantr |
|
12 |
6
|
adantr |
|
13 |
7
|
adantr |
|
14 |
8
|
adantr |
|
15 |
9
|
adantr |
|
16 |
10
|
adantr |
|
17 |
|
simpr |
|
18 |
1 2 3 4 11 12 13 14 15 16 17
|
lsatcvatlem |
|
19 |
5
|
adantr |
|
20 |
6
|
adantr |
|
21 |
8
|
adantr |
|
22 |
7
|
adantr |
|
23 |
9
|
adantr |
|
24 |
|
lveclmod |
|
25 |
5 24
|
syl |
|
26 |
|
lmodabl |
|
27 |
25 26
|
syl |
|
28 |
2
|
lsssssubg |
|
29 |
25 28
|
syl |
|
30 |
2 4 25 7
|
lsatlssel |
|
31 |
29 30
|
sseldd |
|
32 |
2 4 25 8
|
lsatlssel |
|
33 |
29 32
|
sseldd |
|
34 |
3
|
lsmcom |
|
35 |
27 31 33 34
|
syl3anc |
|
36 |
35
|
psseq2d |
|
37 |
10 36
|
mpbid |
|
38 |
37
|
adantr |
|
39 |
|
simpr |
|
40 |
1 2 3 4 19 20 21 22 23 38 39
|
lsatcvatlem |
|
41 |
29 6
|
sseldd |
|
42 |
3
|
lsmlub |
|
43 |
31 33 41 42
|
syl3anc |
|
44 |
|
ssnpss |
|
45 |
43 44
|
syl6bi |
|
46 |
45
|
con2d |
|
47 |
|
ianor |
|
48 |
46 47
|
syl6ib |
|
49 |
10 48
|
mpd |
|
50 |
18 40 49
|
mpjaodan |
|