Step |
Hyp |
Ref |
Expression |
1 |
|
txcn.1 |
|
2 |
|
txcn.2 |
|
3 |
|
txcn.3 |
|
4 |
|
txcn.4 |
|
5 |
|
txcn.5 |
|
6 |
|
txcn.6 |
|
7 |
1
|
toptopon |
|
8 |
2
|
toptopon |
|
9 |
3
|
reseq2i |
|
10 |
5 9
|
eqtri |
|
11 |
|
tx1cn |
|
12 |
10 11
|
eqeltrid |
|
13 |
3
|
reseq2i |
|
14 |
6 13
|
eqtri |
|
15 |
|
tx2cn |
|
16 |
14 15
|
eqeltrid |
|
17 |
|
cnco |
|
18 |
|
cnco |
|
19 |
17 18
|
anim12dan |
|
20 |
19
|
expcom |
|
21 |
12 16 20
|
syl2anc |
|
22 |
7 8 21
|
syl2anb |
|
23 |
22
|
3adant3 |
|
24 |
|
cntop1 |
|
25 |
24
|
ad2antrl |
|
26 |
4
|
topopn |
|
27 |
25 26
|
syl |
|
28 |
4 1
|
cnf |
|
29 |
28
|
ad2antrl |
|
30 |
4 2
|
cnf |
|
31 |
30
|
ad2antll |
|
32 |
10 14
|
upxp |
|
33 |
|
feq3 |
|
34 |
3 33
|
ax-mp |
|
35 |
34
|
3anbi1i |
|
36 |
35
|
eubii |
|
37 |
32 36
|
sylibr |
|
38 |
27 29 31 37
|
syl3anc |
|
39 |
|
euex |
|
40 |
38 39
|
syl |
|
41 |
|
simpll3 |
|
42 |
27
|
adantr |
|
43 |
1
|
topopn |
|
44 |
2
|
topopn |
|
45 |
|
xpexg |
|
46 |
3 45
|
eqeltrid |
|
47 |
43 44 46
|
syl2an |
|
48 |
47
|
3adant3 |
|
49 |
48
|
ad2antrr |
|
50 |
|
fex2 |
|
51 |
41 42 49 50
|
syl3anc |
|
52 |
|
eumo |
|
53 |
38 52
|
syl |
|
54 |
53
|
adantr |
|
55 |
|
simpr |
|
56 |
|
3anass |
|
57 |
|
coeq2 |
|
58 |
|
coeq2 |
|
59 |
57 58
|
jca |
|
60 |
59
|
eqcoms |
|
61 |
60
|
biantrud |
|
62 |
|
feq1 |
|
63 |
61 62
|
bitr3d |
|
64 |
56 63
|
syl5bb |
|
65 |
64
|
moi2 |
|
66 |
51 54 55 41 65
|
syl22anc |
|
67 |
|
eqid |
|
68 |
67 1 2 3 5 6
|
uptx |
|
69 |
68
|
adantl |
|
70 |
|
df-reu |
|
71 |
|
euex |
|
72 |
70 71
|
sylbi |
|
73 |
|
eqid |
|
74 |
4 73
|
cnf |
|
75 |
1 2
|
txuni |
|
76 |
3 75
|
syl5eq |
|
77 |
76
|
3adant3 |
|
78 |
77
|
adantr |
|
79 |
78
|
feq3d |
|
80 |
74 79
|
syl5ibr |
|
81 |
80
|
anim1d |
|
82 |
81 56
|
syl6ibr |
|
83 |
|
simpl |
|
84 |
82 83
|
jca2 |
|
85 |
84
|
eximdv |
|
86 |
72 85
|
syl5 |
|
87 |
69 86
|
mpd |
|
88 |
|
eupick |
|
89 |
38 87 88
|
syl2anc |
|
90 |
89
|
imp |
|
91 |
66 90
|
eqeltrrd |
|
92 |
40 91
|
exlimddv |
|
93 |
92
|
ex |
|
94 |
23 93
|
impbid |
|