Step |
Hyp |
Ref |
Expression |
1 |
|
neipcfilu.x |
|
2 |
|
neipcfilu.j |
|
3 |
|
neipcfilu.u |
|
4 |
|
simp2 |
|
5 |
1 2
|
istps |
|
6 |
4 5
|
sylib |
|
7 |
|
simp3 |
|
8 |
7
|
snssd |
|
9 |
|
snnzg |
|
10 |
7 9
|
syl |
|
11 |
|
neifil |
|
12 |
6 8 10 11
|
syl3anc |
|
13 |
|
filfbas |
|
14 |
12 13
|
syl |
|
15 |
|
eqid |
|
16 |
|
imaeq1 |
|
17 |
16
|
rspceeqv |
|
18 |
15 17
|
mpan2 |
|
19 |
|
vex |
|
20 |
19
|
imaex |
|
21 |
|
eqid |
|
22 |
21
|
elrnmpt |
|
23 |
20 22
|
ax-mp |
|
24 |
18 23
|
sylibr |
|
25 |
24
|
ad2antlr |
|
26 |
1 3 2
|
isusp |
|
27 |
26
|
simplbi |
|
28 |
27
|
3ad2ant1 |
|
29 |
|
eqid |
|
30 |
29
|
utopsnneip |
|
31 |
28 7 30
|
syl2anc |
|
32 |
31
|
eleq2d |
|
33 |
32
|
ad3antrrr |
|
34 |
25 33
|
mpbird |
|
35 |
|
simpl1 |
|
36 |
35
|
3anassrs |
|
37 |
26
|
simprbi |
|
38 |
36 37
|
syl |
|
39 |
38
|
fveq2d |
|
40 |
39
|
fveq1d |
|
41 |
34 40
|
eleqtrrd |
|
42 |
|
simpr |
|
43 |
|
id |
|
44 |
43
|
sqxpeqd |
|
45 |
44
|
sseq1d |
|
46 |
45
|
rspcev |
|
47 |
41 42 46
|
syl2anc |
|
48 |
28
|
adantr |
|
49 |
7
|
adantr |
|
50 |
|
simpr |
|
51 |
|
simpll1 |
|
52 |
|
simplr |
|
53 |
|
ustexsym |
|
54 |
51 52 53
|
syl2anc |
|
55 |
51
|
ad2antrr |
|
56 |
|
simplr |
|
57 |
|
ustssxp |
|
58 |
55 56 57
|
syl2anc |
|
59 |
|
simpll2 |
|
60 |
59
|
3anassrs |
|
61 |
|
ustneism |
|
62 |
58 60 61
|
syl2anc |
|
63 |
|
simprl |
|
64 |
63
|
coeq2d |
|
65 |
|
coss1 |
|
66 |
|
coss2 |
|
67 |
65 66
|
sstrd |
|
68 |
67
|
ad2antll |
|
69 |
|
simpllr |
|
70 |
68 69
|
sstrd |
|
71 |
64 70
|
eqsstrd |
|
72 |
62 71
|
sstrd |
|
73 |
72
|
ex |
|
74 |
73
|
reximdva |
|
75 |
54 74
|
mpd |
|
76 |
|
ustexhalf |
|
77 |
76
|
3adant2 |
|
78 |
75 77
|
r19.29a |
|
79 |
48 49 50 78
|
syl3anc |
|
80 |
47 79
|
r19.29a |
|
81 |
80
|
ralrimiva |
|
82 |
|
iscfilu |
|
83 |
28 82
|
syl |
|
84 |
14 81 83
|
mpbir2and |
|