Step |
Hyp |
Ref |
Expression |
1 |
|
pj1lmhm.l |
|
2 |
|
pj1lmhm.s |
|
3 |
|
pj1lmhm.z |
|
4 |
|
pj1lmhm.p |
|
5 |
|
pj1lmhm.1 |
|
6 |
|
pj1lmhm.2 |
|
7 |
|
pj1lmhm.3 |
|
8 |
|
pj1lmhm.4 |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
1
|
lsssssubg |
|
12 |
5 11
|
syl |
|
13 |
12 6
|
sseldd |
|
14 |
12 7
|
sseldd |
|
15 |
|
lmodabl |
|
16 |
5 15
|
syl |
|
17 |
10 16 13 14
|
ablcntzd |
|
18 |
9 2 3 10 13 14 8 17 4
|
pj1ghm |
|
19 |
|
eqid |
|
20 |
19
|
a1i |
|
21 |
9 2 3 10 13 14 8 17 4
|
pj1id |
|
22 |
21
|
adantrl |
|
23 |
22
|
oveq2d |
|
24 |
5
|
adantr |
|
25 |
|
simprl |
|
26 |
6
|
adantr |
|
27 |
|
eqid |
|
28 |
27 1
|
lssss |
|
29 |
26 28
|
syl |
|
30 |
13
|
adantr |
|
31 |
14
|
adantr |
|
32 |
8
|
adantr |
|
33 |
17
|
adantr |
|
34 |
9 2 3 10 30 31 32 33 4
|
pj1f |
|
35 |
|
simprr |
|
36 |
34 35
|
ffvelrnd |
|
37 |
29 36
|
sseldd |
|
38 |
7
|
adantr |
|
39 |
27 1
|
lssss |
|
40 |
38 39
|
syl |
|
41 |
9 2 3 10 30 31 32 33 4
|
pj2f |
|
42 |
41 35
|
ffvelrnd |
|
43 |
40 42
|
sseldd |
|
44 |
|
eqid |
|
45 |
|
eqid |
|
46 |
27 9 19 44 45
|
lmodvsdi |
|
47 |
24 25 37 43 46
|
syl13anc |
|
48 |
23 47
|
eqtrd |
|
49 |
1 2
|
lsmcl |
|
50 |
5 6 7 49
|
syl3anc |
|
51 |
50
|
adantr |
|
52 |
19 44 45 1
|
lssvscl |
|
53 |
24 51 25 35 52
|
syl22anc |
|
54 |
19 44 45 1
|
lssvscl |
|
55 |
24 26 25 36 54
|
syl22anc |
|
56 |
19 44 45 1
|
lssvscl |
|
57 |
24 38 25 42 56
|
syl22anc |
|
58 |
9 2 3 10 30 31 32 33 4 53 55 57
|
pj1eq |
|
59 |
48 58
|
mpbid |
|
60 |
59
|
simpld |
|
61 |
60
|
ralrimivva |
|
62 |
12 50
|
sseldd |
|
63 |
|
eqid |
|
64 |
63
|
subgbas |
|
65 |
62 64
|
syl |
|
66 |
65
|
raleqdv |
|
67 |
66
|
ralbidv |
|
68 |
61 67
|
mpbid |
|
69 |
63 1
|
lsslmod |
|
70 |
5 50 69
|
syl2anc |
|
71 |
|
ovex |
|
72 |
63 19
|
resssca |
|
73 |
71 72
|
ax-mp |
|
74 |
|
eqid |
|
75 |
63 44
|
ressvsca |
|
76 |
71 75
|
ax-mp |
|
77 |
73 19 45 74 76 44
|
islmhm3 |
|
78 |
70 5 77
|
syl2anc |
|
79 |
18 20 68 78
|
mpbir3and |
|