Step |
Hyp |
Ref |
Expression |
1 |
|
qtoprest.2 |
|
2 |
|
qtoprest.3 |
|
3 |
|
qtoprest.4 |
|
4 |
|
qtoprest.5 |
|
5 |
|
qtoprest.6 |
|
6 |
|
fofn |
|
7 |
2 6
|
syl |
|
8 |
|
qtopid |
|
9 |
1 7 8
|
syl2anc |
|
10 |
|
cnvimass |
|
11 |
7
|
fndmd |
|
12 |
10 11
|
sseqtrid |
|
13 |
4 12
|
eqsstrd |
|
14 |
|
toponuni |
|
15 |
1 14
|
syl |
|
16 |
13 15
|
sseqtrd |
|
17 |
|
eqid |
|
18 |
17
|
cnrest |
|
19 |
9 16 18
|
syl2anc |
|
20 |
|
qtoptopon |
|
21 |
1 2 20
|
syl2anc |
|
22 |
|
df-ima |
|
23 |
4
|
imaeq2d |
|
24 |
|
foimacnv |
|
25 |
2 3 24
|
syl2anc |
|
26 |
23 25
|
eqtrd |
|
27 |
22 26
|
syl5eqr |
|
28 |
|
eqimss |
|
29 |
27 28
|
syl |
|
30 |
|
cnrest2 |
|
31 |
21 29 3 30
|
syl3anc |
|
32 |
19 31
|
mpbid |
|
33 |
|
resttopon |
|
34 |
21 3 33
|
syl2anc |
|
35 |
|
qtopss |
|
36 |
32 34 27 35
|
syl3anc |
|
37 |
|
resttopon |
|
38 |
1 13 37
|
syl2anc |
|
39 |
|
fnfun |
|
40 |
7 39
|
syl |
|
41 |
13 11
|
sseqtrrd |
|
42 |
|
fores |
|
43 |
40 41 42
|
syl2anc |
|
44 |
|
foeq3 |
|
45 |
26 44
|
syl |
|
46 |
43 45
|
mpbid |
|
47 |
|
elqtop3 |
|
48 |
38 46 47
|
syl2anc |
|
49 |
|
cnvresima |
|
50 |
|
imass2 |
|
51 |
50
|
adantl |
|
52 |
4
|
adantr |
|
53 |
51 52
|
sseqtrrd |
|
54 |
|
df-ss |
|
55 |
53 54
|
sylib |
|
56 |
49 55
|
syl5eq |
|
57 |
56
|
eleq1d |
|
58 |
|
simplrl |
|
59 |
|
df-ss |
|
60 |
58 59
|
sylib |
|
61 |
|
topontop |
|
62 |
21 61
|
syl |
|
63 |
62
|
ad2antrr |
|
64 |
|
toponmax |
|
65 |
1 64
|
syl |
|
66 |
|
fornex |
|
67 |
65 2 66
|
sylc |
|
68 |
67 3
|
ssexd |
|
69 |
68
|
ad2antrr |
|
70 |
3
|
ad2antrr |
|
71 |
58 70
|
sstrd |
|
72 |
|
topontop |
|
73 |
1 72
|
syl |
|
74 |
|
restopn2 |
|
75 |
73 74
|
sylan |
|
76 |
75
|
simprbda |
|
77 |
76
|
adantrl |
|
78 |
77
|
an32s |
|
79 |
|
elqtop3 |
|
80 |
1 2 79
|
syl2anc |
|
81 |
80
|
ad2antrr |
|
82 |
71 78 81
|
mpbir2and |
|
83 |
|
elrestr |
|
84 |
63 69 82 83
|
syl3anc |
|
85 |
60 84
|
eqeltrrd |
|
86 |
34
|
ad2antrr |
|
87 |
|
toponuni |
|
88 |
86 87
|
syl |
|
89 |
88
|
difeq1d |
|
90 |
3
|
ad2antrr |
|
91 |
21
|
ad2antrr |
|
92 |
|
toponuni |
|
93 |
91 92
|
syl |
|
94 |
90 93
|
sseqtrd |
|
95 |
90
|
ssdifssd |
|
96 |
40
|
ad2antrr |
|
97 |
|
funcnvcnv |
|
98 |
|
imadif |
|
99 |
96 97 98
|
3syl |
|
100 |
4
|
ad2antrr |
|
101 |
100
|
difeq1d |
|
102 |
99 101
|
eqtr4d |
|
103 |
|
simpr |
|
104 |
38
|
ad2antrr |
|
105 |
|
toponuni |
|
106 |
104 105
|
syl |
|
107 |
106
|
difeq1d |
|
108 |
|
topontop |
|
109 |
104 108
|
syl |
|
110 |
|
simplrr |
|
111 |
|
eqid |
|
112 |
111
|
opncld |
|
113 |
109 110 112
|
syl2anc |
|
114 |
107 113
|
eqeltrd |
|
115 |
|
restcldr |
|
116 |
103 114 115
|
syl2anc |
|
117 |
102 116
|
eqeltrd |
|
118 |
|
qtopcld |
|
119 |
1 2 118
|
syl2anc |
|
120 |
119
|
ad2antrr |
|
121 |
95 117 120
|
mpbir2and |
|
122 |
|
difssd |
|
123 |
|
eqid |
|
124 |
123
|
restcldi |
|
125 |
94 121 122 124
|
syl3anc |
|
126 |
89 125
|
eqeltrrd |
|
127 |
|
topontop |
|
128 |
86 127
|
syl |
|
129 |
|
simplrl |
|
130 |
129 88
|
sseqtrd |
|
131 |
|
eqid |
|
132 |
131
|
isopn2 |
|
133 |
128 130 132
|
syl2anc |
|
134 |
126 133
|
mpbird |
|
135 |
5
|
adantr |
|
136 |
85 134 135
|
mpjaodan |
|
137 |
136
|
expr |
|
138 |
57 137
|
sylbid |
|
139 |
138
|
expimpd |
|
140 |
48 139
|
sylbid |
|
141 |
140
|
ssrdv |
|
142 |
36 141
|
eqssd |
|