Step |
Hyp |
Ref |
Expression |
1 |
|
pt1hmeo.j |
|
2 |
|
pt1hmeo.a |
|
3 |
|
pt1hmeo.r |
|
4 |
|
fconstmpt |
|
5 |
2
|
adantr |
|
6 |
|
sneq |
|
7 |
6
|
xpeq1d |
|
8 |
|
opeq1 |
|
9 |
8
|
sneqd |
|
10 |
7 9
|
eqeq12d |
|
11 |
|
vex |
|
12 |
|
vex |
|
13 |
11 12
|
xpsn |
|
14 |
10 13
|
vtoclg |
|
15 |
5 14
|
syl |
|
16 |
4 15
|
syl5eqr |
|
17 |
16
|
mpteq2dva |
|
18 |
|
snex |
|
19 |
18
|
a1i |
|
20 |
|
topontop |
|
21 |
3 20
|
syl |
|
22 |
2 21
|
fsnd |
|
23 |
3
|
cnmptid |
|
24 |
23
|
adantr |
|
25 |
|
elsni |
|
26 |
25
|
fveq2d |
|
27 |
|
fvsng |
|
28 |
2 3 27
|
syl2anc |
|
29 |
26 28
|
sylan9eqr |
|
30 |
29
|
oveq2d |
|
31 |
24 30
|
eleqtrrd |
|
32 |
1 3 19 22 31
|
ptcn |
|
33 |
17 32
|
eqeltrrd |
|
34 |
|
simprr |
|
35 |
16
|
adantrr |
|
36 |
34 35
|
eqtr4d |
|
37 |
|
simprl |
|
38 |
37
|
adantr |
|
39 |
38
|
fmpttd |
|
40 |
|
toponmax |
|
41 |
3 40
|
syl |
|
42 |
41
|
adantr |
|
43 |
|
elmapg |
|
44 |
42 18 43
|
sylancl |
|
45 |
39 44
|
mpbird |
|
46 |
36 45
|
eqeltrd |
|
47 |
34
|
fveq1d |
|
48 |
2
|
adantr |
|
49 |
|
fvsng |
|
50 |
48 37 49
|
syl2anc |
|
51 |
47 50
|
eqtr2d |
|
52 |
46 51
|
jca |
|
53 |
|
simprr |
|
54 |
|
simprl |
|
55 |
41
|
adantr |
|
56 |
|
elmapg |
|
57 |
55 18 56
|
sylancl |
|
58 |
54 57
|
mpbid |
|
59 |
|
snidg |
|
60 |
2 59
|
syl |
|
61 |
60
|
adantr |
|
62 |
58 61
|
ffvelrnd |
|
63 |
53 62
|
eqeltrd |
|
64 |
2
|
adantr |
|
65 |
|
fsn2g |
|
66 |
64 65
|
syl |
|
67 |
58 66
|
mpbid |
|
68 |
67
|
simprd |
|
69 |
53
|
opeq2d |
|
70 |
69
|
sneqd |
|
71 |
68 70
|
eqtr4d |
|
72 |
63 71
|
jca |
|
73 |
52 72
|
impbida |
|
74 |
73
|
mptcnv |
|
75 |
|
xpsng |
|
76 |
2 3 75
|
syl2anc |
|
77 |
76
|
eqcomd |
|
78 |
77
|
fveq2d |
|
79 |
1 78
|
syl5eq |
|
80 |
|
eqid |
|
81 |
80
|
pttoponconst |
|
82 |
19 3 81
|
syl2anc |
|
83 |
79 82
|
eqeltrd |
|
84 |
|
toponuni |
|
85 |
83 84
|
syl |
|
86 |
85
|
mpteq1d |
|
87 |
74 86
|
eqtrd |
|
88 |
|
eqid |
|
89 |
88 1
|
ptpjcn |
|
90 |
18 22 60 89
|
mp3an2i |
|
91 |
28
|
oveq2d |
|
92 |
90 91
|
eleqtrd |
|
93 |
87 92
|
eqeltrd |
|
94 |
|
ishmeo |
|
95 |
33 93 94
|
sylanbrc |
|