Step |
Hyp |
Ref |
Expression |
1 |
|
cncfuni.acn |
|
2 |
|
cncfuni.f |
|
3 |
|
cncfuni.auni |
|
4 |
|
cncfuni.opn |
|
5 |
|
cncfuni.fcn |
|
6 |
3
|
sselda |
|
7 |
|
eluni2 |
|
8 |
6 7
|
sylib |
|
9 |
|
simp1l |
|
10 |
|
simp2 |
|
11 |
|
elin |
|
12 |
11
|
biimpri |
|
13 |
12
|
adantll |
|
14 |
13
|
3adant2 |
|
15 |
2
|
fdmd |
|
16 |
15
|
ineq2d |
|
17 |
|
incom |
|
18 |
16 17
|
eqtr2di |
|
19 |
18
|
reseq2d |
|
20 |
|
frel |
|
21 |
2 20
|
syl |
|
22 |
|
resindm |
|
23 |
21 22
|
syl |
|
24 |
19 23
|
eqtrd |
|
25 |
|
inss1 |
|
26 |
25
|
a1i |
|
27 |
26 1
|
sstrd |
|
28 |
|
ssidd |
|
29 |
|
eqid |
|
30 |
|
eqid |
|
31 |
29
|
cnfldtop |
|
32 |
|
unicntop |
|
33 |
32
|
restid |
|
34 |
31 33
|
ax-mp |
|
35 |
34
|
eqcomi |
|
36 |
29 30 35
|
cncfcn |
|
37 |
27 28 36
|
syl2anc |
|
38 |
37
|
eqcomd |
|
39 |
24 38
|
eleq12d |
|
40 |
39
|
adantr |
|
41 |
5 40
|
mpbird |
|
42 |
41
|
3adant3 |
|
43 |
29
|
cnfldtopon |
|
44 |
43
|
a1i |
|
45 |
|
resttopon |
|
46 |
44 27 45
|
syl2anc |
|
47 |
46
|
3ad2ant1 |
|
48 |
43
|
a1i |
|
49 |
|
cncnp |
|
50 |
47 48 49
|
syl2anc |
|
51 |
42 50
|
mpbid |
|
52 |
51
|
simprd |
|
53 |
|
simp3 |
|
54 |
|
rspa |
|
55 |
52 53 54
|
syl2anc |
|
56 |
31
|
a1i |
|
57 |
|
cnex |
|
58 |
57
|
ssex |
|
59 |
1 58
|
syl |
|
60 |
|
restabs |
|
61 |
56 26 59 60
|
syl3anc |
|
62 |
61
|
eqcomd |
|
63 |
62
|
oveq1d |
|
64 |
63
|
fveq1d |
|
65 |
64
|
3ad2ant1 |
|
66 |
55 65
|
eleqtrd |
|
67 |
|
resttop |
|
68 |
56 59 67
|
syl2anc |
|
69 |
68
|
3ad2ant1 |
|
70 |
32
|
restuni |
|
71 |
56 1 70
|
syl2anc |
|
72 |
26 71
|
sseqtrd |
|
73 |
72
|
3ad2ant1 |
|
74 |
4
|
3adant3 |
|
75 |
|
eqid |
|
76 |
75
|
isopn3 |
|
77 |
69 73 76
|
syl2anc |
|
78 |
74 77
|
mpbid |
|
79 |
78
|
eqcomd |
|
80 |
53 79
|
eleqtrd |
|
81 |
71
|
feq2d |
|
82 |
2 81
|
mpbid |
|
83 |
82
|
3ad2ant1 |
|
84 |
75 32
|
cnprest |
|
85 |
69 73 80 83 84
|
syl22anc |
|
86 |
66 85
|
mpbird |
|
87 |
9 10 14 86
|
syl3anc |
|
88 |
87
|
rexlimdv3a |
|
89 |
8 88
|
mpd |
|
90 |
89
|
ralrimiva |
|
91 |
|
resttopon |
|
92 |
44 1 91
|
syl2anc |
|
93 |
|
cncnp |
|
94 |
92 44 93
|
syl2anc |
|
95 |
2 90 94
|
mpbir2and |
|
96 |
|
eqid |
|
97 |
29 96 35
|
cncfcn |
|
98 |
1 28 97
|
syl2anc |
|
99 |
98
|
eqcomd |
|
100 |
95 99
|
eleqtrd |
|