Step |
Hyp |
Ref |
Expression |
1 |
|
vex |
|
2 |
1
|
elintrab |
|
3 |
|
filsspw |
|
4 |
3
|
3ad2ant1 |
|
5 |
|
difss |
|
6 |
|
filtop |
|
7 |
|
difexg |
|
8 |
6 7
|
syl |
|
9 |
8
|
3ad2ant1 |
|
10 |
|
elpwg |
|
11 |
9 10
|
syl |
|
12 |
5 11
|
mpbiri |
|
13 |
12
|
snssd |
|
14 |
4 13
|
unssd |
|
15 |
|
ssun1 |
|
16 |
|
filn0 |
|
17 |
|
ssn0 |
|
18 |
15 16 17
|
sylancr |
|
19 |
18
|
3ad2ant1 |
|
20 |
|
elsni |
|
21 |
|
filelss |
|
22 |
21
|
3adant3 |
|
23 |
|
reldisj |
|
24 |
22 23
|
syl |
|
25 |
|
dfss4 |
|
26 |
25
|
biimpi |
|
27 |
26
|
sseq2d |
|
28 |
27
|
3ad2ant3 |
|
29 |
24 28
|
bitrd |
|
30 |
|
filss |
|
31 |
30
|
3exp2 |
|
32 |
31
|
3imp |
|
33 |
29 32
|
sylbid |
|
34 |
33
|
necon3bd |
|
35 |
34
|
3exp |
|
36 |
35
|
com24 |
|
37 |
36
|
3imp1 |
|
38 |
|
ineq2 |
|
39 |
38
|
neeq1d |
|
40 |
37 39
|
syl5ibrcom |
|
41 |
40
|
expimpd |
|
42 |
20 41
|
sylan2i |
|
43 |
42
|
ralrimivv |
|
44 |
|
filfbas |
|
45 |
44
|
3ad2ant1 |
|
46 |
5
|
a1i |
|
47 |
26
|
3ad2ant2 |
|
48 |
|
difeq2 |
|
49 |
|
dif0 |
|
50 |
48 49
|
eqtrdi |
|
51 |
50
|
3ad2ant3 |
|
52 |
47 51
|
eqtr3d |
|
53 |
6
|
3ad2ant1 |
|
54 |
52 53
|
eqeltrd |
|
55 |
54
|
3expia |
|
56 |
55
|
necon3bd |
|
57 |
56
|
ex |
|
58 |
57
|
com23 |
|
59 |
58
|
3imp |
|
60 |
6
|
3ad2ant1 |
|
61 |
|
snfbas |
|
62 |
46 59 60 61
|
syl3anc |
|
63 |
|
fbunfip |
|
64 |
45 62 63
|
syl2anc |
|
65 |
43 64
|
mpbird |
|
66 |
|
fsubbas |
|
67 |
6 66
|
syl |
|
68 |
67
|
3ad2ant1 |
|
69 |
14 19 65 68
|
mpbir3and |
|
70 |
|
fgcl |
|
71 |
69 70
|
syl |
|
72 |
|
filssufil |
|
73 |
|
snex |
|
74 |
|
unexg |
|
75 |
73 74
|
mpan2 |
|
76 |
|
ssfii |
|
77 |
75 76
|
syl |
|
78 |
77
|
3ad2ant1 |
|
79 |
78
|
unssad |
|
80 |
|
ssfg |
|
81 |
69 80
|
syl |
|
82 |
79 81
|
sstrd |
|
83 |
82
|
ad2antrr |
|
84 |
|
simpr |
|
85 |
83 84
|
sstrd |
|
86 |
|
ufilfil |
|
87 |
|
0nelfil |
|
88 |
86 87
|
syl |
|
89 |
88
|
ad2antlr |
|
90 |
|
disjdif |
|
91 |
86
|
ad2antlr |
|
92 |
|
simprr |
|
93 |
77
|
unssbd |
|
94 |
93
|
3ad2ant1 |
|
95 |
94
|
adantr |
|
96 |
69
|
adantr |
|
97 |
96 80
|
syl |
|
98 |
95 97
|
sstrd |
|
99 |
98
|
adantr |
|
100 |
|
simprl |
|
101 |
99 100
|
sstrd |
|
102 |
|
snidg |
|
103 |
8 102
|
syl |
|
104 |
103
|
3ad2ant1 |
|
105 |
104
|
ad2antrr |
|
106 |
101 105
|
sseldd |
|
107 |
|
filin |
|
108 |
91 92 106 107
|
syl3anc |
|
109 |
90 108
|
eqeltrrid |
|
110 |
109
|
expr |
|
111 |
89 110
|
mtod |
|
112 |
85 111
|
jca |
|
113 |
112
|
exp31 |
|
114 |
113
|
reximdvai |
|
115 |
72 114
|
syl5 |
|
116 |
71 115
|
mpd |
|
117 |
116
|
3expia |
|
118 |
|
filssufil |
|
119 |
|
filelss |
|
120 |
119
|
ex |
|
121 |
86 120
|
syl |
|
122 |
121
|
con3d |
|
123 |
122
|
impcom |
|
124 |
123
|
a1d |
|
125 |
124
|
ancld |
|
126 |
125
|
reximdva |
|
127 |
118 126
|
syl5com |
|
128 |
127
|
adantr |
|
129 |
117 128
|
pm2.61d |
|
130 |
129
|
ex |
|
131 |
|
rexanali |
|
132 |
130 131
|
syl6ib |
|
133 |
132
|
con4d |
|
134 |
2 133
|
syl5bi |
|
135 |
134
|
ssrdv |
|
136 |
|
ssintub |
|
137 |
136
|
a1i |
|
138 |
135 137
|
eqssd |
|