Step |
Hyp |
Ref |
Expression |
1 |
|
perfdvf.1 |
|
2 |
|
df-dv |
|
3 |
2
|
dmmpossx |
|
4 |
|
simpl |
|
5 |
3 4
|
sseldi |
|
6 |
|
oveq2 |
|
7 |
6
|
opeliunxp2 |
|
8 |
5 7
|
sylib |
|
9 |
8
|
simprd |
|
10 |
|
cnex |
|
11 |
8
|
simpld |
|
12 |
|
elpm2g |
|
13 |
10 11 12
|
sylancr |
|
14 |
9 13
|
mpbid |
|
15 |
14
|
simpld |
|
16 |
15
|
adantr |
|
17 |
3
|
sseli |
|
18 |
17 7
|
sylib |
|
19 |
18
|
simprd |
|
20 |
18
|
simpld |
|
21 |
10 20 12
|
sylancr |
|
22 |
19 21
|
mpbid |
|
23 |
22
|
simprd |
|
24 |
23
|
adantr |
|
25 |
11
|
elpwid |
|
26 |
24 25
|
sstrd |
|
27 |
26
|
adantr |
|
28 |
1
|
cnfldtopon |
|
29 |
|
resttopon |
|
30 |
28 25 29
|
sylancr |
|
31 |
|
topontop |
|
32 |
30 31
|
syl |
|
33 |
|
toponuni |
|
34 |
30 33
|
syl |
|
35 |
24 34
|
sseqtrd |
|
36 |
|
eqid |
|
37 |
36
|
ntrss2 |
|
38 |
32 35 37
|
syl2anc |
|
39 |
38
|
sselda |
|
40 |
16 27 39
|
dvlem |
|
41 |
40
|
fmpttd |
|
42 |
27
|
ssdifssd |
|
43 |
36
|
ntrss3 |
|
44 |
32 35 43
|
syl2anc |
|
45 |
44 34
|
sseqtrrd |
|
46 |
|
restabs |
|
47 |
28 45 11 46
|
mp3an2i |
|
48 |
|
simpr |
|
49 |
36
|
ntropn |
|
50 |
32 35 49
|
syl2anc |
|
51 |
|
eqid |
|
52 |
36 51
|
perfopn |
|
53 |
48 50 52
|
syl2anc |
|
54 |
47 53
|
eqeltrrd |
|
55 |
1
|
cnfldtop |
|
56 |
45 25
|
sstrd |
|
57 |
28
|
toponunii |
|
58 |
|
eqid |
|
59 |
57 58
|
restperf |
|
60 |
55 56 59
|
sylancr |
|
61 |
54 60
|
mpbid |
|
62 |
57
|
lpss3 |
|
63 |
55 26 38 62
|
mp3an2i |
|
64 |
61 63
|
sstrd |
|
65 |
64
|
sselda |
|
66 |
57
|
lpdifsn |
|
67 |
55 27 66
|
sylancr |
|
68 |
65 67
|
mpbid |
|
69 |
41 42 68 1
|
limcmo |
|
70 |
69
|
ex |
|
71 |
|
moanimv |
|
72 |
70 71
|
sylibr |
|
73 |
|
eqid |
|
74 |
|
eqid |
|
75 |
73 1 74 25 15 24
|
eldv |
|
76 |
75
|
mobidv |
|
77 |
72 76
|
mpbird |
|
78 |
77
|
alrimiv |
|
79 |
|
reldv |
|
80 |
|
dffun6 |
|
81 |
79 80
|
mpbiran |
|
82 |
78 81
|
sylibr |
|
83 |
82
|
funfnd |
|
84 |
|
vex |
|
85 |
84
|
elrn |
|
86 |
25 15 24
|
dvcl |
|
87 |
86
|
ex |
|
88 |
87
|
exlimdv |
|
89 |
85 88
|
syl5bi |
|
90 |
89
|
ssrdv |
|
91 |
|
df-f |
|
92 |
83 90 91
|
sylanbrc |
|
93 |
92
|
ex |
|
94 |
|
f0 |
|
95 |
|
df-ov |
|
96 |
|
ndmfv |
|
97 |
95 96
|
syl5eq |
|
98 |
97
|
dmeqd |
|
99 |
|
dm0 |
|
100 |
98 99
|
eqtrdi |
|
101 |
97 100
|
feq12d |
|
102 |
94 101
|
mpbiri |
|
103 |
102
|
a1d |
|
104 |
93 103
|
pm2.61i |
|