Step |
Hyp |
Ref |
Expression |
1 |
|
dvh3dim.h |
|
2 |
|
dvh3dim.u |
|
3 |
|
dvh3dim.v |
|
4 |
|
dvh3dim.n |
|
5 |
|
dvh3dim.k |
|
6 |
|
dvh3dim.x |
|
7 |
|
dvh3dim.y |
|
8 |
|
dvh3dim2.z |
|
9 |
|
dvh3dim3.t |
|
10 |
|
eqid |
|
11 |
1 2 5
|
dvhlmod |
|
12 |
11
|
adantr |
|
13 |
3 10 4 11 8 9
|
lspprcl |
|
14 |
13
|
adantr |
|
15 |
|
simpr |
|
16 |
3 4 11 8 9
|
lspprid2 |
|
17 |
16
|
adantr |
|
18 |
10 4 12 14 15 17
|
lspprss |
|
19 |
|
sspss |
|
20 |
18 19
|
sylib |
|
21 |
1 2 5
|
dvhlvec |
|
22 |
21
|
adantr |
|
23 |
3 10 4 11 7 9
|
lspprcl |
|
24 |
23
|
adantr |
|
25 |
8
|
adantr |
|
26 |
9
|
adantr |
|
27 |
|
simpr |
|
28 |
3 10 4 22 24 25 26 27
|
lspprat |
|
29 |
5
|
3ad2ant1 |
|
30 |
|
simp2 |
|
31 |
6
|
3ad2ant1 |
|
32 |
8
|
3ad2ant1 |
|
33 |
1 2 3 4 29 30 31 32
|
dvh3dim2 |
|
34 |
11
|
3ad2ant1 |
|
35 |
10
|
lsssssubg |
|
36 |
34 35
|
syl |
|
37 |
3 10 4
|
lspsncl |
|
38 |
11 6 37
|
syl2anc |
|
39 |
38
|
3ad2ant1 |
|
40 |
36 39
|
sseldd |
|
41 |
3 10 4
|
lspsncl |
|
42 |
34 30 41
|
syl2anc |
|
43 |
36 42
|
sseldd |
|
44 |
|
prssi |
|
45 |
7 9 44
|
syl2anc |
|
46 |
|
snsspr1 |
|
47 |
46
|
a1i |
|
48 |
3 4
|
lspss |
|
49 |
11 45 47 48
|
syl3anc |
|
50 |
49
|
3ad2ant1 |
|
51 |
|
simp3 |
|
52 |
50 51
|
sseqtrd |
|
53 |
|
eqid |
|
54 |
53
|
lsmless2 |
|
55 |
40 43 52 54
|
syl3anc |
|
56 |
3 4 53 11 6 7
|
lsmpr |
|
57 |
56
|
3ad2ant1 |
|
58 |
|
prcom |
|
59 |
58
|
fveq2i |
|
60 |
3 4 53 34 31 30
|
lsmpr |
|
61 |
59 60
|
syl5eq |
|
62 |
55 57 61
|
3sstr4d |
|
63 |
62
|
ssneld |
|
64 |
3 10 4
|
lspsncl |
|
65 |
11 8 64
|
syl2anc |
|
66 |
65
|
3ad2ant1 |
|
67 |
36 66
|
sseldd |
|
68 |
|
snsspr2 |
|
69 |
68
|
a1i |
|
70 |
3 4
|
lspss |
|
71 |
11 45 69 70
|
syl3anc |
|
72 |
71
|
3ad2ant1 |
|
73 |
72 51
|
sseqtrd |
|
74 |
53
|
lsmless2 |
|
75 |
67 43 73 74
|
syl3anc |
|
76 |
3 4 53 11 8 9
|
lsmpr |
|
77 |
76
|
3ad2ant1 |
|
78 |
|
prcom |
|
79 |
78
|
fveq2i |
|
80 |
3 4 53 34 32 30
|
lsmpr |
|
81 |
79 80
|
syl5eq |
|
82 |
75 77 81
|
3sstr4d |
|
83 |
82
|
ssneld |
|
84 |
63 83
|
anim12d |
|
85 |
84
|
reximdv |
|
86 |
33 85
|
mpd |
|
87 |
86
|
rexlimdv3a |
|
88 |
87
|
adantr |
|
89 |
28 88
|
mpd |
|
90 |
1 2 3 4 5 7 6 9
|
dvh3dim2 |
|
91 |
90
|
adantr |
|
92 |
|
simpr |
|
93 |
|
prcom |
|
94 |
93
|
fveq2i |
|
95 |
94
|
eleq2i |
|
96 |
95
|
notbii |
|
97 |
96
|
a1i |
|
98 |
|
eleq2 |
|
99 |
98
|
notbid |
|
100 |
97 99
|
anbi12d |
|
101 |
92 100
|
syl |
|
102 |
101
|
rexbidv |
|
103 |
91 102
|
mpbid |
|
104 |
89 103
|
jaodan |
|
105 |
20 104
|
syldan |
|
106 |
1 2 3 4 5 7 6 9
|
dvh3dim2 |
|
107 |
106
|
adantr |
|
108 |
|
simpl1l |
|
109 |
108 11
|
syl |
|
110 |
|
simpl2 |
|
111 |
108 7
|
syl |
|
112 |
|
eqid |
|
113 |
3 112
|
lmodvacl |
|
114 |
109 110 111 113
|
syl3anc |
|
115 |
3 10 4 11 6 7
|
lspprcl |
|
116 |
108 115
|
syl |
|
117 |
3 4 11 6 7
|
lspprid2 |
|
118 |
108 117
|
syl |
|
119 |
|
simpl3l |
|
120 |
94
|
eleq2i |
|
121 |
119 120
|
sylnib |
|
122 |
3 112 10 109 116 118 110 121
|
lssvancl2 |
|
123 |
108 13
|
syl |
|
124 |
|
simpr |
|
125 |
|
simpl1r |
|
126 |
3 112 10 109 123 124 111 125
|
lssvancl1 |
|
127 |
|
eleq1 |
|
128 |
127
|
notbid |
|
129 |
|
eleq1 |
|
130 |
129
|
notbid |
|
131 |
128 130
|
anbi12d |
|
132 |
131
|
rspcev |
|
133 |
114 122 126 132
|
syl12anc |
|
134 |
|
simpl2 |
|
135 |
|
simpl3l |
|
136 |
135 120
|
sylnib |
|
137 |
|
simpr |
|
138 |
|
eleq1 |
|
139 |
138
|
notbid |
|
140 |
|
eleq1 |
|
141 |
140
|
notbid |
|
142 |
139 141
|
anbi12d |
|
143 |
142
|
rspcev |
|
144 |
134 136 137 143
|
syl12anc |
|
145 |
133 144
|
pm2.61dan |
|
146 |
145
|
rexlimdv3a |
|
147 |
107 146
|
mpd |
|
148 |
105 147
|
pm2.61dan |
|