Step |
Hyp |
Ref |
Expression |
1 |
|
lshpsmreu.v |
|
2 |
|
lshpsmreu.a |
|
3 |
|
lshpsmreu.n |
|
4 |
|
lshpsmreu.p |
|
5 |
|
lshpsmreu.h |
|
6 |
|
lshpsmreu.w |
|
7 |
|
lshpsmreu.u |
|
8 |
|
lshpsmreu.z |
|
9 |
|
lshpsmreu.x |
|
10 |
|
lshpsmreu.e |
|
11 |
|
lshpsmreu.d |
|
12 |
|
lshpsmreu.k |
|
13 |
|
lshpsmreu.t |
|
14 |
9 10
|
eleqtrrd |
|
15 |
|
lveclmod |
|
16 |
6 15
|
syl |
|
17 |
|
eqid |
|
18 |
17
|
lsssssubg |
|
19 |
16 18
|
syl |
|
20 |
17 5 16 7
|
lshplss |
|
21 |
19 20
|
sseldd |
|
22 |
1 17 3
|
lspsncl |
|
23 |
16 8 22
|
syl2anc |
|
24 |
19 23
|
sseldd |
|
25 |
2 4
|
lsmelval |
|
26 |
21 24 25
|
syl2anc |
|
27 |
14 26
|
mpbid |
|
28 |
|
df-rex |
|
29 |
11 12 1 13 3
|
lspsnel |
|
30 |
16 8 29
|
syl2anc |
|
31 |
30
|
anbi1d |
|
32 |
|
r19.41v |
|
33 |
31 32
|
bitr4di |
|
34 |
33
|
exbidv |
|
35 |
|
rexcom4 |
|
36 |
|
ovex |
|
37 |
|
oveq2 |
|
38 |
37
|
eqeq2d |
|
39 |
36 38
|
ceqsexv |
|
40 |
39
|
rexbii |
|
41 |
35 40
|
bitr3i |
|
42 |
34 41
|
bitrdi |
|
43 |
28 42
|
syl5bb |
|
44 |
43
|
rexbidv |
|
45 |
27 44
|
mpbid |
|
46 |
|
rexcom |
|
47 |
45 46
|
sylib |
|
48 |
|
oveq1 |
|
49 |
48
|
eqeq2d |
|
50 |
49
|
cbvrexvw |
|
51 |
|
eqid |
|
52 |
|
eqid |
|
53 |
|
simp11l |
|
54 |
53 21
|
syl |
|
55 |
53 24
|
syl |
|
56 |
1 51 3 4 5 6 7 8 10
|
lshpdisj |
|
57 |
53 56
|
syl |
|
58 |
53 6
|
syl |
|
59 |
58 15
|
syl |
|
60 |
|
lmodabl |
|
61 |
59 60
|
syl |
|
62 |
52 61 54 55
|
ablcntzd |
|
63 |
|
simp12 |
|
64 |
|
simp2 |
|
65 |
|
simp1rl |
|
66 |
65
|
3ad2ant1 |
|
67 |
53 8
|
syl |
|
68 |
1 13 11 12 3 59 66 67
|
lspsneli |
|
69 |
|
simp1rr |
|
70 |
69
|
3ad2ant1 |
|
71 |
1 13 11 12 3 59 70 67
|
lspsneli |
|
72 |
|
simp13 |
|
73 |
|
simp3 |
|
74 |
72 73
|
eqtr3d |
|
75 |
2 51 52 54 55 57 62 63 64 68 71 74
|
subgdisj2 |
|
76 |
53 7
|
syl |
|
77 |
53 10
|
syl |
|
78 |
1 3 4 5 51 59 76 67 77
|
lshpne0 |
|
79 |
1 13 11 12 51 58 66 70 67 78
|
lvecvscan2 |
|
80 |
75 79
|
mpbid |
|
81 |
80
|
rexlimdv3a |
|
82 |
81
|
rexlimdv3a |
|
83 |
50 82
|
syl5bi |
|
84 |
83
|
impd |
|
85 |
84
|
ralrimivva |
|
86 |
|
oveq1 |
|
87 |
86
|
oveq2d |
|
88 |
87
|
eqeq2d |
|
89 |
88
|
rexbidv |
|
90 |
89
|
reu4 |
|
91 |
47 85 90
|
sylanbrc |
|
92 |
|
oveq1 |
|
93 |
92
|
oveq2d |
|
94 |
93
|
eqeq2d |
|
95 |
94
|
rexbidv |
|
96 |
95
|
cbvreuvw |
|
97 |
|
oveq1 |
|
98 |
97
|
eqeq2d |
|
99 |
98
|
cbvrexvw |
|
100 |
99
|
reubii |
|
101 |
96 100
|
bitri |
|
102 |
91 101
|
sylib |
|