Step |
Hyp |
Ref |
Expression |
1 |
|
lfl1dim.v |
|
2 |
|
lfl1dim.d |
|
3 |
|
lfl1dim.f |
|
4 |
|
lfl1dim.l |
|
5 |
|
lfl1dim.k |
|
6 |
|
lfl1dim.t |
|
7 |
|
lfl1dim.w |
|
8 |
|
lfl1dim.g |
|
9 |
|
df-rab |
|
10 |
|
lveclmod |
|
11 |
7 10
|
syl |
|
12 |
|
eqid |
|
13 |
2 5 12
|
lmod0cl |
|
14 |
11 13
|
syl |
|
15 |
14
|
ad2antrr |
|
16 |
|
simpr |
|
17 |
11
|
ad2antrr |
|
18 |
8
|
ad2antrr |
|
19 |
1 2 3 5 6 12 17 18
|
lfl0sc |
|
20 |
16 19
|
eqtr4d |
|
21 |
|
sneq |
|
22 |
21
|
xpeq2d |
|
23 |
22
|
oveq2d |
|
24 |
23
|
rspceeqv |
|
25 |
15 20 24
|
syl2anc |
|
26 |
25
|
a1d |
|
27 |
14
|
ad3antrrr |
|
28 |
11
|
ad3antrrr |
|
29 |
|
simpllr |
|
30 |
1 3 4 28 29
|
lkrssv |
|
31 |
11
|
adantr |
|
32 |
8
|
adantr |
|
33 |
2 12 1 3 4
|
lkr0f |
|
34 |
31 32 33
|
syl2anc |
|
35 |
34
|
biimpar |
|
36 |
35
|
sseq1d |
|
37 |
36
|
biimpa |
|
38 |
30 37
|
eqssd |
|
39 |
2 12 1 3 4
|
lkr0f |
|
40 |
28 29 39
|
syl2anc |
|
41 |
38 40
|
mpbid |
|
42 |
8
|
ad3antrrr |
|
43 |
1 2 3 5 6 12 28 42
|
lfl0sc |
|
44 |
41 43
|
eqtr4d |
|
45 |
27 44 24
|
syl2anc |
|
46 |
45
|
ex |
|
47 |
|
eqid |
|
48 |
7
|
ad2antrr |
|
49 |
8
|
ad2antrr |
|
50 |
|
simprr |
|
51 |
1 2 12 47 3 4
|
lkrshp |
|
52 |
48 49 50 51
|
syl3anc |
|
53 |
|
simplr |
|
54 |
|
simprl |
|
55 |
1 2 12 47 3 4
|
lkrshp |
|
56 |
48 53 54 55
|
syl3anc |
|
57 |
47 48 52 56
|
lshpcmp |
|
58 |
7
|
ad3antrrr |
|
59 |
8
|
ad3antrrr |
|
60 |
|
simpllr |
|
61 |
|
simpr |
|
62 |
2 5 6 1 3 4
|
eqlkr2 |
|
63 |
58 59 60 61 62
|
syl121anc |
|
64 |
63
|
ex |
|
65 |
57 64
|
sylbid |
|
66 |
26 46 65
|
pm2.61da2ne |
|
67 |
7
|
ad2antrr |
|
68 |
8
|
ad2antrr |
|
69 |
|
simpr |
|
70 |
1 2 5 6 3 4 67 68 69
|
lkrscss |
|
71 |
70
|
ex |
|
72 |
|
fveq2 |
|
73 |
72
|
sseq2d |
|
74 |
73
|
biimprcd |
|
75 |
71 74
|
syl6 |
|
76 |
75
|
rexlimdv |
|
77 |
66 76
|
impbid |
|
78 |
77
|
pm5.32da |
|
79 |
11
|
adantr |
|
80 |
8
|
adantr |
|
81 |
|
simpr |
|
82 |
1 2 5 6 3 79 80 81
|
lflvscl |
|
83 |
|
eleq1a |
|
84 |
82 83
|
syl |
|
85 |
84
|
pm4.71rd |
|
86 |
85
|
rexbidva |
|
87 |
|
r19.42v |
|
88 |
86 87
|
bitr2di |
|
89 |
78 88
|
bitrd |
|
90 |
89
|
abbidv |
|
91 |
9 90
|
syl5eq |
|