Step |
Hyp |
Ref |
Expression |
1 |
|
topdifinf.t |
|
2 |
|
nfv |
|
3 |
|
nfab1 |
|
4 |
|
nfcv |
|
5 |
|
abid |
|
6 |
|
df-rex |
|
7 |
5 6
|
bitri |
|
8 |
|
eqid |
|
9 |
|
snex |
|
10 |
|
snelpwi |
|
11 |
|
eleq1 |
|
12 |
10 11
|
syl5ibr |
|
13 |
12
|
imdistani |
|
14 |
13
|
anim2i |
|
15 |
14
|
3impb |
|
16 |
|
3anass |
|
17 |
15 16
|
sylibr |
|
18 |
|
snfi |
|
19 |
|
eleq1 |
|
20 |
18 19
|
mpbiri |
|
21 |
|
difinf |
|
22 |
20 21
|
sylan2 |
|
23 |
22
|
orcd |
|
24 |
23
|
anim2i |
|
25 |
24
|
ancoms |
|
26 |
25
|
3impa |
|
27 |
17 26
|
syl |
|
28 |
1
|
rabeq2i |
|
29 |
27 28
|
sylibr |
|
30 |
|
eleq1 |
|
31 |
30
|
3ad2ant2 |
|
32 |
29 31
|
mpbid |
|
33 |
32
|
sbcth |
|
34 |
9 33
|
ax-mp |
|
35 |
|
sbcimg |
|
36 |
9 35
|
ax-mp |
|
37 |
34 36
|
mpbi |
|
38 |
|
sbc3an |
|
39 |
|
sbcg |
|
40 |
9 39
|
ax-mp |
|
41 |
40
|
3anbi1i |
|
42 |
|
eqsbc3 |
|
43 |
9 42
|
ax-mp |
|
44 |
43
|
3anbi2i |
|
45 |
38 41 44
|
3bitri |
|
46 |
|
sbcg |
|
47 |
9 46
|
ax-mp |
|
48 |
47
|
3anbi3i |
|
49 |
45 48
|
bitri |
|
50 |
|
sbcg |
|
51 |
9 50
|
ax-mp |
|
52 |
37 49 51
|
3imtr3i |
|
53 |
8 52
|
mp3an2 |
|
54 |
53
|
ex |
|
55 |
54
|
pm4.71d |
|
56 |
55
|
anbi1d |
|
57 |
56
|
exbidv |
|
58 |
7 57
|
syl5bb |
|
59 |
|
anass |
|
60 |
59
|
exbii |
|
61 |
|
exsimpr |
|
62 |
60 61
|
sylbi |
|
63 |
58 62
|
syl6bi |
|
64 |
|
ancom |
|
65 |
|
eleq1 |
|
66 |
65
|
pm5.32i |
|
67 |
64 66
|
bitr4i |
|
68 |
67
|
exbii |
|
69 |
63 68
|
syl6ib |
|
70 |
|
exsimpr |
|
71 |
69 70
|
syl6 |
|
72 |
|
ax5e |
|
73 |
71 72
|
syl6 |
|
74 |
2 3 4 73
|
ssrd |
|
75 |
|
eqid |
|
76 |
75
|
dissneq |
|
77 |
74 76
|
sylan |
|
78 |
|
nfielex |
|
79 |
78
|
adantr |
|
80 |
|
difss |
|
81 |
|
elfvex |
|
82 |
|
difexg |
|
83 |
|
elpwg |
|
84 |
81 82 83
|
3syl |
|
85 |
80 84
|
mpbiri |
|
86 |
85
|
adantl |
|
87 |
|
difinf |
|
88 |
18 87
|
mpan2 |
|
89 |
|
0fin |
|
90 |
|
eleq1 |
|
91 |
89 90
|
mpbiri |
|
92 |
88 91
|
nsyl |
|
93 |
92
|
ad2antrl |
|
94 |
|
vsnid |
|
95 |
|
inelcm |
|
96 |
94 95
|
mpan2 |
|
97 |
|
disj4 |
|
98 |
97
|
necon2abii |
|
99 |
96 98
|
sylibr |
|
100 |
99
|
pssned |
|
101 |
100
|
adantr |
|
102 |
101
|
neneqd |
|
103 |
93 102
|
jca |
|
104 |
|
pm4.56 |
|
105 |
103 104
|
sylib |
|
106 |
|
difeq2 |
|
107 |
106
|
eleq1d |
|
108 |
107
|
notbid |
|
109 |
|
eqeq1 |
|
110 |
|
eqeq1 |
|
111 |
109 110
|
orbi12d |
|
112 |
108 111
|
orbi12d |
|
113 |
112 1
|
elrab2 |
|
114 |
85
|
biantrurd |
|
115 |
113 114
|
bitr4id |
|
116 |
|
dfin4 |
|
117 |
|
inss2 |
|
118 |
|
ssfi |
|
119 |
18 117 118
|
mp2an |
|
120 |
116 119
|
eqeltrri |
|
121 |
|
biortn |
|
122 |
120 121
|
ax-mp |
|
123 |
115 122
|
bitr4di |
|
124 |
123
|
ad2antll |
|
125 |
105 124
|
mtbird |
|
126 |
125
|
expcom |
|
127 |
|
nelneq2 |
|
128 |
|
eqcom |
|
129 |
127 128
|
sylnibr |
|
130 |
86 126 129
|
syl6an |
|
131 |
79 130
|
exellimddv |
|
132 |
77 131
|
pm2.65da |
|
133 |
132
|
con4i |
|