Step |
Hyp |
Ref |
Expression |
1 |
|
dvco.f |
|
2 |
|
dvco.x |
|
3 |
|
dvco.g |
|
4 |
|
dvco.y |
|
5 |
|
dvcobr.s |
|
6 |
|
dvcobr.t |
|
7 |
|
dvco.bf |
|
8 |
|
dvco.bg |
|
9 |
|
dvco.j |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
2 5
|
sstrd |
|
13 |
3 12
|
fssd |
|
14 |
10 9 11 6 13 4
|
eldv |
|
15 |
8 14
|
mpbid |
|
16 |
15
|
simpld |
|
17 |
5 1 2
|
dvcl |
|
18 |
7 17
|
mpdan |
|
19 |
18
|
ad2antrr |
|
20 |
1
|
adantr |
|
21 |
|
eldifi |
|
22 |
|
ffvelcdm |
|
23 |
3 21 22
|
syl2an |
|
24 |
20 23
|
ffvelcdmd |
|
25 |
24
|
adantr |
|
26 |
3
|
adantr |
|
27 |
6 13 4
|
dvbss |
|
28 |
|
reldv |
|
29 |
|
releldm |
|
30 |
28 8 29
|
sylancr |
|
31 |
27 30
|
sseldd |
|
32 |
31
|
adantr |
|
33 |
26 32
|
ffvelcdmd |
|
34 |
20 33
|
ffvelcdmd |
|
35 |
34
|
adantr |
|
36 |
25 35
|
subcld |
|
37 |
13
|
ad2antrr |
|
38 |
21
|
ad2antlr |
|
39 |
37 38
|
ffvelcdmd |
|
40 |
31
|
ad2antrr |
|
41 |
37 40
|
ffvelcdmd |
|
42 |
39 41
|
subcld |
|
43 |
|
simpr |
|
44 |
39 41
|
subeq0ad |
|
45 |
44
|
necon3abid |
|
46 |
43 45
|
mpbird |
|
47 |
36 42 46
|
divcld |
|
48 |
19 47
|
ifclda |
|
49 |
4 6
|
sstrd |
|
50 |
13 49 31
|
dvlem |
|
51 |
|
ssidd |
|
52 |
9
|
cnfldtopon |
|
53 |
|
txtopon |
|
54 |
52 52 53
|
mp2an |
|
55 |
54
|
toponrestid |
|
56 |
23
|
anim1i |
|
57 |
|
eldifsn |
|
58 |
56 57
|
sylibr |
|
59 |
58
|
anasss |
|
60 |
|
eldifsni |
|
61 |
|
ifnefalse |
|
62 |
60 61
|
syl |
|
63 |
62
|
adantl |
|
64 |
3 31
|
ffvelcdmd |
|
65 |
1 12 64
|
dvlem |
|
66 |
63 65
|
eqeltrd |
|
67 |
|
limcresi |
|
68 |
3
|
feqmptd |
|
69 |
68
|
reseq1d |
|
70 |
|
difss |
|
71 |
|
resmpt |
|
72 |
70 71
|
ax-mp |
|
73 |
69 72
|
eqtrdi |
|
74 |
73
|
oveq1d |
|
75 |
67 74
|
sseqtrid |
|
76 |
|
eqid |
|
77 |
76 9
|
dvcnp2 |
|
78 |
6 13 4 30 77
|
syl31anc |
|
79 |
9 76
|
cnplimc |
|
80 |
49 31 79
|
syl2anc |
|
81 |
78 80
|
mpbid |
|
82 |
81
|
simprd |
|
83 |
75 82
|
sseldd |
|
84 |
|
eqid |
|
85 |
|
eqid |
|
86 |
84 9 85 5 1 2
|
eldv |
|
87 |
7 86
|
mpbid |
|
88 |
87
|
simprd |
|
89 |
62
|
mpteq2ia |
|
90 |
89
|
oveq1i |
|
91 |
88 90
|
eleqtrrdi |
|
92 |
|
eqeq1 |
|
93 |
|
fveq2 |
|
94 |
93
|
oveq1d |
|
95 |
|
oveq1 |
|
96 |
94 95
|
oveq12d |
|
97 |
92 96
|
ifbieq2d |
|
98 |
|
iftrue |
|
99 |
98
|
ad2antll |
|
100 |
59 66 83 91 97 99
|
limcco |
|
101 |
15
|
simprd |
|
102 |
9
|
mpomulcn |
|
103 |
6 13 4
|
dvcl |
|
104 |
8 103
|
mpdan |
|
105 |
18 104
|
opelxpd |
|
106 |
54
|
toponunii |
|
107 |
106
|
cncnpi |
|
108 |
102 105 107
|
sylancr |
|
109 |
48 50 51 51 9 55 100 101 108
|
limccnp2 |
|
110 |
|
df-mpt |
|
111 |
110
|
oveq1i |
|
112 |
109 111
|
eleqtrdi |
|
113 |
|
ovmpot |
|
114 |
18 104 113
|
syl2anc |
|
115 |
|
ovmpot |
|
116 |
48 50 115
|
syl2anc |
|
117 |
116
|
eqeq2d |
|
118 |
117
|
pm5.32da |
|
119 |
118
|
opabbidv |
|
120 |
|
df-mpt |
|
121 |
120
|
eqcomi |
|
122 |
121
|
eqeq2i |
|
123 |
122
|
biimpi |
|
124 |
123
|
oveq1d |
|
125 |
119 124
|
syl |
|
126 |
112 114 125
|
3eltr3d |
|
127 |
|
oveq1 |
|
128 |
127
|
eqeq1d |
|
129 |
|
oveq1 |
|
130 |
129
|
eqeq1d |
|
131 |
19
|
mul01d |
|
132 |
12
|
adantr |
|
133 |
132 23
|
sseldd |
|
134 |
132 33
|
sseldd |
|
135 |
133 134
|
subeq0ad |
|
136 |
135
|
biimpar |
|
137 |
136
|
oveq1d |
|
138 |
49
|
adantr |
|
139 |
21
|
adantl |
|
140 |
138 139
|
sseldd |
|
141 |
138 32
|
sseldd |
|
142 |
140 141
|
subcld |
|
143 |
|
eldifsni |
|
144 |
143
|
adantl |
|
145 |
140 141 144
|
subne0d |
|
146 |
142 145
|
div0d |
|
147 |
146
|
adantr |
|
148 |
137 147
|
eqtrd |
|
149 |
148
|
oveq2d |
|
150 |
|
fveq2 |
|
151 |
24 34
|
subeq0ad |
|
152 |
150 151
|
imbitrrid |
|
153 |
152
|
imp |
|
154 |
153
|
oveq1d |
|
155 |
154 147
|
eqtrd |
|
156 |
131 149 155
|
3eqtr4d |
|
157 |
142
|
adantr |
|
158 |
145
|
adantr |
|
159 |
36 42 157 46 158
|
dmdcan2d |
|
160 |
128 130 156 159
|
ifbothda |
|
161 |
|
fvco3 |
|
162 |
3 21 161
|
syl2an |
|
163 |
3 31
|
fvco3d |
|
164 |
163
|
adantr |
|
165 |
162 164
|
oveq12d |
|
166 |
165
|
oveq1d |
|
167 |
160 166
|
eqtr4d |
|
168 |
167
|
mpteq2dva |
|
169 |
168
|
oveq1d |
|
170 |
126 169
|
eleqtrd |
|
171 |
|
eqid |
|
172 |
1 3
|
fcod |
|
173 |
10 9 171 6 172 4
|
eldv |
|
174 |
16 170 173
|
mpbir2and |
|