Step |
Hyp |
Ref |
Expression |
1 |
|
filnet.h |
|
2 |
|
filnet.d |
|
3 |
1 2
|
filnetlem3 |
|
4 |
3
|
simpri |
|
5 |
4
|
simprd |
|
6 |
|
f2ndres |
|
7 |
4
|
simpld |
|
8 |
|
fssres2 |
|
9 |
6 7 8
|
sylancr |
|
10 |
|
filtop |
|
11 |
|
xpexg |
|
12 |
10 11
|
mpdan |
|
13 |
12 7
|
ssexd |
|
14 |
|
fex |
|
15 |
9 13 14
|
syl2anc |
|
16 |
3
|
simpli |
|
17 |
|
dirdm |
|
18 |
5 17
|
syl |
|
19 |
16 18
|
eqtr4id |
|
20 |
19
|
feq2d |
|
21 |
9 20
|
mpbid |
|
22 |
|
eqid |
|
23 |
22
|
tailf |
|
24 |
5 23
|
syl |
|
25 |
19
|
feq2d |
|
26 |
24 25
|
mpbird |
|
27 |
26
|
adantr |
|
28 |
|
ffn |
|
29 |
|
imaeq2 |
|
30 |
29
|
sseq1d |
|
31 |
30
|
rexrn |
|
32 |
27 28 31
|
3syl |
|
33 |
|
fo2nd |
|
34 |
|
fofn |
|
35 |
33 34
|
ax-mp |
|
36 |
|
ssv |
|
37 |
|
fnssres |
|
38 |
35 36 37
|
mp2an |
|
39 |
|
fnfun |
|
40 |
38 39
|
ax-mp |
|
41 |
27
|
ffvelrnda |
|
42 |
41
|
elpwid |
|
43 |
19
|
ad2antrr |
|
44 |
42 43
|
sseqtrrd |
|
45 |
38
|
fndmi |
|
46 |
44 45
|
sseqtrrdi |
|
47 |
|
funimass4 |
|
48 |
40 46 47
|
sylancr |
|
49 |
5
|
ad2antrr |
|
50 |
|
simpr |
|
51 |
50 43
|
eleqtrd |
|
52 |
|
vex |
|
53 |
52
|
a1i |
|
54 |
22
|
eltail |
|
55 |
49 51 53 54
|
syl3anc |
|
56 |
50
|
biantrurd |
|
57 |
56
|
anbi1d |
|
58 |
|
vex |
|
59 |
1 2 58 52
|
filnetlem1 |
|
60 |
57 59
|
bitr4di |
|
61 |
55 60
|
bitr4d |
|
62 |
61
|
imbi1d |
|
63 |
|
fvres |
|
64 |
63
|
eleq1d |
|
65 |
64
|
adantr |
|
66 |
65
|
pm5.74i |
|
67 |
|
impexp |
|
68 |
66 67
|
bitri |
|
69 |
62 68
|
bitrdi |
|
70 |
69
|
ralbidv2 |
|
71 |
48 70
|
bitrd |
|
72 |
71
|
rexbidva |
|
73 |
|
vex |
|
74 |
|
vex |
|
75 |
73 74
|
op1std |
|
76 |
75
|
sseq1d |
|
77 |
73 74
|
op2ndd |
|
78 |
77
|
eleq1d |
|
79 |
76 78
|
imbi12d |
|
80 |
79
|
raliunxp |
|
81 |
|
sneq |
|
82 |
|
id |
|
83 |
81 82
|
xpeq12d |
|
84 |
83
|
cbviunv |
|
85 |
1 84
|
eqtri |
|
86 |
85
|
raleqi |
|
87 |
|
dfss3 |
|
88 |
87
|
imbi2i |
|
89 |
|
r19.21v |
|
90 |
88 89
|
bitr4i |
|
91 |
90
|
ralbii |
|
92 |
80 86 91
|
3bitr4i |
|
93 |
92
|
rexbii |
|
94 |
1
|
rexeqi |
|
95 |
|
vex |
|
96 |
|
vex |
|
97 |
95 96
|
op1std |
|
98 |
97
|
sseq2d |
|
99 |
98
|
imbi1d |
|
100 |
99
|
ralbidv |
|
101 |
100
|
rexiunxp |
|
102 |
93 94 101
|
3bitri |
|
103 |
|
fileln0 |
|
104 |
103
|
adantlr |
|
105 |
|
r19.9rzv |
|
106 |
104 105
|
syl |
|
107 |
|
ssid |
|
108 |
|
sseq1 |
|
109 |
|
sseq1 |
|
110 |
108 109
|
imbi12d |
|
111 |
110
|
rspcv |
|
112 |
107 111
|
mpii |
|
113 |
112
|
adantl |
|
114 |
|
sstr2 |
|
115 |
114
|
com12 |
|
116 |
115
|
ralrimivw |
|
117 |
113 116
|
impbid1 |
|
118 |
106 117
|
bitr3d |
|
119 |
118
|
rexbidva |
|
120 |
102 119
|
syl5bb |
|
121 |
32 72 120
|
3bitrd |
|
122 |
121
|
pm5.32da |
|
123 |
|
filn0 |
|
124 |
95
|
snnz |
|
125 |
103 124
|
jctil |
|
126 |
|
neanior |
|
127 |
125 126
|
sylib |
|
128 |
|
ss0b |
|
129 |
|
xpeq0 |
|
130 |
128 129
|
bitri |
|
131 |
127 130
|
sylnibr |
|
132 |
131
|
ralrimiva |
|
133 |
|
r19.2z |
|
134 |
123 132 133
|
syl2anc |
|
135 |
|
rexnal |
|
136 |
134 135
|
sylib |
|
137 |
1
|
sseq1i |
|
138 |
|
ss0b |
|
139 |
|
iunss |
|
140 |
137 138 139
|
3bitr3i |
|
141 |
140
|
necon3abii |
|
142 |
136 141
|
sylibr |
|
143 |
|
dmresi |
|
144 |
1 2
|
filnetlem2 |
|
145 |
144
|
simpli |
|
146 |
|
dmss |
|
147 |
145 146
|
ax-mp |
|
148 |
143 147
|
eqsstrri |
|
149 |
144
|
simpri |
|
150 |
|
dmss |
|
151 |
149 150
|
ax-mp |
|
152 |
|
dmxpid |
|
153 |
151 152
|
sseqtri |
|
154 |
148 153
|
eqssi |
|
155 |
154
|
tailfb |
|
156 |
5 142 155
|
syl2anc |
|
157 |
|
elfm |
|
158 |
10 156 9 157
|
syl3anc |
|
159 |
|
filfbas |
|
160 |
|
elfg |
|
161 |
159 160
|
syl |
|
162 |
122 158 161
|
3bitr4d |
|
163 |
162
|
eqrdv |
|
164 |
|
fgfil |
|
165 |
163 164
|
eqtr2d |
|
166 |
21 165
|
jca |
|
167 |
|
feq1 |
|
168 |
|
oveq2 |
|
169 |
168
|
fveq1d |
|
170 |
169
|
eqeq2d |
|
171 |
167 170
|
anbi12d |
|
172 |
171
|
spcegv |
|
173 |
15 166 172
|
sylc |
|
174 |
|
dmeq |
|
175 |
174
|
feq2d |
|
176 |
|
fveq2 |
|
177 |
176
|
rneqd |
|
178 |
177
|
fveq2d |
|
179 |
178
|
eqeq2d |
|
180 |
175 179
|
anbi12d |
|
181 |
180
|
exbidv |
|
182 |
181
|
rspcev |
|
183 |
5 173 182
|
syl2anc |
|