Step |
Hyp |
Ref |
Expression |
1 |
|
cvmcov.1 |
|
2 |
|
n0 |
|
3 |
|
simpl2 |
|
4 |
|
simpl1 |
|
5 |
|
cvmtop1 |
|
6 |
4 5
|
syl |
|
7 |
6
|
adantr |
|
8 |
1
|
cvmsss |
|
9 |
8
|
adantl |
|
10 |
9
|
sselda |
|
11 |
|
cvmcn |
|
12 |
4 11
|
syl |
|
13 |
|
cnima |
|
14 |
12 3 13
|
syl2anc |
|
15 |
14
|
adantr |
|
16 |
|
inopn |
|
17 |
7 10 15 16
|
syl3anc |
|
18 |
17
|
fmpttd |
|
19 |
18
|
frnd |
|
20 |
1
|
cvmsn0 |
|
21 |
20
|
adantl |
|
22 |
|
dmmptg |
|
23 |
|
inex1g |
|
24 |
22 23
|
mprg |
|
25 |
24
|
eqeq1i |
|
26 |
|
dm0rn0 |
|
27 |
25 26
|
bitr3i |
|
28 |
27
|
necon3bii |
|
29 |
21 28
|
sylib |
|
30 |
19 29
|
jca |
|
31 |
|
inss2 |
|
32 |
|
elpw2g |
|
33 |
15 32
|
syl |
|
34 |
31 33
|
mpbiri |
|
35 |
34
|
fmpttd |
|
36 |
35
|
frnd |
|
37 |
|
sspwuni |
|
38 |
36 37
|
sylib |
|
39 |
|
simpl3 |
|
40 |
|
imass2 |
|
41 |
39 40
|
syl |
|
42 |
1
|
cvmsuni |
|
43 |
42
|
adantl |
|
44 |
41 43
|
sseqtrrd |
|
45 |
44
|
sselda |
|
46 |
|
eqid |
|
47 |
|
ineq1 |
|
48 |
47
|
rspceeqv |
|
49 |
46 48
|
mpan2 |
|
50 |
49
|
ad2antrl |
|
51 |
|
vex |
|
52 |
51
|
inex1 |
|
53 |
|
eqid |
|
54 |
53
|
elrnmpt |
|
55 |
52 54
|
ax-mp |
|
56 |
50 55
|
sylibr |
|
57 |
|
simprr |
|
58 |
|
simplr |
|
59 |
57 58
|
elind |
|
60 |
|
eleq2 |
|
61 |
60
|
rspcev |
|
62 |
56 59 61
|
syl2anc |
|
63 |
62
|
rexlimdvaa |
|
64 |
|
eluni2 |
|
65 |
|
eluni2 |
|
66 |
63 64 65
|
3imtr4g |
|
67 |
45 66
|
mpd |
|
68 |
38 67
|
eqelssd |
|
69 |
|
eldifsn |
|
70 |
|
vex |
|
71 |
53
|
elrnmpt |
|
72 |
70 71
|
ax-mp |
|
73 |
47
|
equcoms |
|
74 |
73
|
necon3ai |
|
75 |
|
simpllr |
|
76 |
|
simplr |
|
77 |
|
simpr |
|
78 |
1
|
cvmsdisj |
|
79 |
75 76 77 78
|
syl3anc |
|
80 |
79
|
ord |
|
81 |
|
inss1 |
|
82 |
|
sseq0 |
|
83 |
81 82
|
mpan |
|
84 |
74 80 83
|
syl56 |
|
85 |
|
neeq1 |
|
86 |
|
ineq2 |
|
87 |
|
inindir |
|
88 |
86 87
|
eqtr4di |
|
89 |
88
|
eqeq1d |
|
90 |
85 89
|
imbi12d |
|
91 |
84 90
|
syl5ibrcom |
|
92 |
91
|
rexlimdva |
|
93 |
72 92
|
syl5bi |
|
94 |
93
|
impd |
|
95 |
69 94
|
syl5bi |
|
96 |
95
|
ralrimiv |
|
97 |
|
inss1 |
|
98 |
|
resabs1 |
|
99 |
97 98
|
ax-mp |
|
100 |
1
|
cvmshmeo |
|
101 |
100
|
adantll |
|
102 |
6
|
adantr |
|
103 |
9
|
sselda |
|
104 |
|
elssuni |
|
105 |
103 104
|
syl |
|
106 |
|
eqid |
|
107 |
106
|
restuni |
|
108 |
102 105 107
|
syl2anc |
|
109 |
97 108
|
sseqtrid |
|
110 |
|
eqid |
|
111 |
110
|
hmeores |
|
112 |
101 109 111
|
syl2anc |
|
113 |
99 112
|
eqeltrrid |
|
114 |
97
|
a1i |
|
115 |
|
simpr |
|
116 |
|
restabs |
|
117 |
102 114 115 116
|
syl3anc |
|
118 |
|
incom |
|
119 |
|
cnvresima |
|
120 |
118 119
|
eqtr4i |
|
121 |
120
|
imaeq2i |
|
122 |
4
|
adantr |
|
123 |
|
simplr |
|
124 |
1
|
cvmsf1o |
|
125 |
122 123 115 124
|
syl3anc |
|
126 |
|
f1ofo |
|
127 |
125 126
|
syl |
|
128 |
39
|
adantr |
|
129 |
|
foimacnv |
|
130 |
127 128 129
|
syl2anc |
|
131 |
121 130
|
syl5eq |
|
132 |
131
|
oveq2d |
|
133 |
|
cvmtop2 |
|
134 |
4 133
|
syl |
|
135 |
1
|
cvmsrcl |
|
136 |
135
|
adantl |
|
137 |
|
restabs |
|
138 |
134 39 136 137
|
syl3anc |
|
139 |
138
|
adantr |
|
140 |
132 139
|
eqtrd |
|
141 |
117 140
|
oveq12d |
|
142 |
113 141
|
eleqtrd |
|
143 |
96 142
|
jca |
|
144 |
143
|
ralrimiva |
|
145 |
52
|
rgenw |
|
146 |
47
|
cbvmptv |
|
147 |
|
sneq |
|
148 |
147
|
difeq2d |
|
149 |
|
ineq1 |
|
150 |
149
|
eqeq1d |
|
151 |
148 150
|
raleqbidv |
|
152 |
|
reseq2 |
|
153 |
|
oveq2 |
|
154 |
153
|
oveq1d |
|
155 |
152 154
|
eleq12d |
|
156 |
151 155
|
anbi12d |
|
157 |
146 156
|
ralrnmptw |
|
158 |
145 157
|
ax-mp |
|
159 |
144 158
|
sylibr |
|
160 |
68 159
|
jca |
|
161 |
1
|
cvmscbv |
|
162 |
161
|
cvmsval |
|
163 |
6 162
|
syl |
|
164 |
3 30 160 163
|
mpbir3and |
|
165 |
164
|
ne0d |
|
166 |
165
|
ex |
|
167 |
166
|
exlimdv |
|
168 |
2 167
|
syl5bi |
|