Step | Hyp | Ref
| Expression |
1 | | cntop1 12359 |
. . . 4
|
2 | 1 | a1i 9 |
. . 3
TopOn
|
3 | | eqid 2137 |
. . . . . . . 8
|
4 | | eqid 2137 |
. . . . . . . 8
|
5 | 3, 4 | cnf 12362 |
. . . . . . 7
|
6 | 5 | ffnd 5268 |
. . . . . 6
|
7 | 6 | a1i 9 |
. . . . 5
TopOn
|
8 | | simp2 982 |
. . . . 5
TopOn |
9 | 7, 8 | jctird 315 |
. . . 4
TopOn
|
10 | | df-f 5122 |
. . . 4
|
11 | 9, 10 | syl6ibr 161 |
. . 3
TopOn
|
12 | 2, 11 | jcad 305 |
. 2
TopOn
|
13 | | cntop1 12359 |
. . . . 5
↾t
|
14 | 13 | adantl 275 |
. . . 4
TopOn ↾t |
15 | 3 | toptopon 12174 |
. . . . . 6
TopOn |
16 | 14, 15 | sylib 121 |
. . . . 5
TopOn ↾t TopOn |
17 | | resttopon 12329 |
. . . . . . 7
TopOn ↾t TopOn |
18 | 17 | 3adant2 1000 |
. . . . . 6
TopOn ↾t TopOn |
19 | 18 | adantr 274 |
. . . . 5
TopOn ↾t ↾t TopOn |
20 | | simpr 109 |
. . . . 5
TopOn ↾t ↾t |
21 | | cnf2 12363 |
. . . . 5
TopOn ↾t TopOn ↾t |
22 | 16, 19, 20, 21 | syl3anc 1216 |
. . . 4
TopOn ↾t |
23 | 14, 22 | jca 304 |
. . 3
TopOn ↾t
|
24 | 23 | ex 114 |
. 2
TopOn
↾t |
25 | | vex 2684 |
. . . . . . . . 9
|
26 | 25 | inex1 4057 |
. . . . . . . 8
|
27 | 26 | a1i 9 |
. . . . . . 7
TopOn
|
28 | | simpl1 984 |
. . . . . . . 8
TopOn
TopOn |
29 | | toponmax 12181 |
. . . . . . . . . 10
TopOn
|
30 | 28, 29 | syl 14 |
. . . . . . . . 9
TopOn
|
31 | | simpl3 986 |
. . . . . . . . 9
TopOn
|
32 | 30, 31 | ssexd 4063 |
. . . . . . . 8
TopOn
|
33 | | elrest 12116 |
. . . . . . . 8
TopOn ↾t
|
34 | 28, 32, 33 | syl2anc 408 |
. . . . . . 7
TopOn
↾t
|
35 | | imaeq2 4872 |
. . . . . . . . 9
|
36 | 35 | eleq1d 2206 |
. . . . . . . 8
|
37 | 36 | adantl 275 |
. . . . . . 7
TopOn
|
38 | 27, 34, 37 | ralxfr2d 4380 |
. . . . . 6
TopOn
↾t |
39 | | simplrr 525 |
. . . . . . . . . 10
TopOn
|
40 | | ffun 5270 |
. . . . . . . . . 10
|
41 | | inpreima 5539 |
. . . . . . . . . 10
|
42 | 39, 40, 41 | 3syl 17 |
. . . . . . . . 9
TopOn
|
43 | | cnvimass 4897 |
. . . . . . . . . . . 12
|
44 | | cnvimarndm 4898 |
. . . . . . . . . . . 12
|
45 | 43, 44 | sseqtrri 3127 |
. . . . . . . . . . 11
|
46 | | simpll2 1021 |
. . . . . . . . . . . 12
TopOn
|
47 | | imass2 4910 |
. . . . . . . . . . . 12
|
48 | 46, 47 | syl 14 |
. . . . . . . . . . 11
TopOn
|
49 | 45, 48 | sstrid 3103 |
. . . . . . . . . 10
TopOn
|
50 | | df-ss 3079 |
. . . . . . . . . 10
|
51 | 49, 50 | sylib 121 |
. . . . . . . . 9
TopOn
|
52 | 42, 51 | eqtrd 2170 |
. . . . . . . 8
TopOn
|
53 | 52 | eleq1d 2206 |
. . . . . . 7
TopOn
|
54 | 53 | ralbidva 2431 |
. . . . . 6
TopOn
|
55 | | simprr 521 |
. . . . . . . 8
TopOn
|
56 | 55, 31 | fssd 5280 |
. . . . . . 7
TopOn
|
57 | 56 | biantrurd 303 |
. . . . . 6
TopOn
|
58 | 38, 54, 57 | 3bitrrd 214 |
. . . . 5
TopOn
↾t |
59 | 55 | biantrurd 303 |
. . . . 5
TopOn
↾t
↾t |
60 | 58, 59 | bitrd 187 |
. . . 4
TopOn
↾t |
61 | | simprl 520 |
. . . . . 6
TopOn
|
62 | 61, 15 | sylib 121 |
. . . . 5
TopOn
TopOn |
63 | | iscn 12355 |
. . . . 5
TopOn TopOn
|
64 | 62, 28, 63 | syl2anc 408 |
. . . 4
TopOn
|
65 | 18 | adantr 274 |
. . . . 5
TopOn
↾t TopOn |
66 | | iscn 12355 |
. . . . 5
TopOn ↾t TopOn ↾t
↾t |
67 | 62, 65, 66 | syl2anc 408 |
. . . 4
TopOn
↾t
↾t |
68 | 60, 64, 67 | 3bitr4d 219 |
. . 3
TopOn
↾t |
69 | 68 | ex 114 |
. 2
TopOn
↾t |
70 | 12, 24, 69 | pm5.21ndd 694 |
1
TopOn
↾t |