Step | Hyp | Ref
| Expression |
1 | | simpr 477 |
. . . . . . 7
|
2 | | simplr1 1103 |
. . . . . . . . . 10
|
3 | | n0 3931 |
. . . . . . . . . . 11
|
4 | | inss2 3834 |
. . . . . . . . . . . . . 14
|
5 | 4 | sseli 3599 |
. . . . . . . . . . . . 13
|
6 | | eliun 4524 |
. . . . . . . . . . . . . 14
|
7 | | rexn0 4074 |
. . . . . . . . . . . . . 14
|
8 | 6, 7 | sylbi 207 |
. . . . . . . . . . . . 13
|
9 | 5, 8 | syl 17 |
. . . . . . . . . . . 12
|
10 | 9 | exlimiv 1858 |
. . . . . . . . . . 11
|
11 | 3, 10 | sylbi 207 |
. . . . . . . . . 10
|
12 | 2, 11 | syl 17 |
. . . . . . . . 9
|
13 | | simplll 798 |
. . . . . . . . . 10
|
14 | | iunconn.4 |
. . . . . . . . . . 11
|
15 | 14 | ralrimiva 2966 |
. . . . . . . . . 10
|
16 | 13, 15 | syl 17 |
. . . . . . . . 9
|
17 | | r19.2z 4060 |
. . . . . . . . 9
|
18 | 12, 16, 17 | syl2anc 693 |
. . . . . . . 8
|
19 | | eliun 4524 |
. . . . . . . 8
|
20 | 18, 19 | sylibr 224 |
. . . . . . 7
|
21 | 1, 20 | sseldd 3604 |
. . . . . 6
|
22 | | elun 3753 |
. . . . . 6
|
23 | 21, 22 | sylib 208 |
. . . . 5
|
24 | | iunconn.2 |
. . . . . . . 8
TopOn |
25 | 13, 24 | syl 17 |
. . . . . . 7
TopOn |
26 | | iunconn.3 |
. . . . . . . 8
|
27 | 13, 26 | sylan 488 |
. . . . . . 7
|
28 | 13, 14 | sylan 488 |
. . . . . . 7
|
29 | | iunconn.5 |
. . . . . . . 8
↾t Conn |
30 | 13, 29 | sylan 488 |
. . . . . . 7
↾t Conn |
31 | | simpllr 799 |
. . . . . . . 8
|
32 | 31 | simpld 475 |
. . . . . . 7
|
33 | 31 | simprd 479 |
. . . . . . 7
|
34 | | simplr2 1104 |
. . . . . . 7
|
35 | | simplr3 1105 |
. . . . . . 7
|
36 | | nfv 1843 |
. . . . . . . . 9
|
37 | | nfcv 2764 |
. . . . . . . . . . . 12
|
38 | | nfiu1 4550 |
. . . . . . . . . . . 12
|
39 | 37, 38 | nfin 3820 |
. . . . . . . . . . 11
|
40 | | nfcv 2764 |
. . . . . . . . . . 11
|
41 | 39, 40 | nfne 2894 |
. . . . . . . . . 10
|
42 | | nfcv 2764 |
. . . . . . . . . . . 12
|
43 | 42, 38 | nfin 3820 |
. . . . . . . . . . 11
|
44 | 43, 40 | nfne 2894 |
. . . . . . . . . 10
|
45 | | nfcv 2764 |
. . . . . . . . . . 11
|
46 | | nfcv 2764 |
. . . . . . . . . . . 12
|
47 | 46, 38 | nfdif 3731 |
. . . . . . . . . . 11
|
48 | 45, 47 | nfss 3596 |
. . . . . . . . . 10
|
49 | 41, 44, 48 | nf3an 1831 |
. . . . . . . . 9
|
50 | 36, 49 | nfan 1828 |
. . . . . . . 8
|
51 | 37, 42 | nfun 3769 |
. . . . . . . . 9
|
52 | 38, 51 | nfss 3596 |
. . . . . . . 8
|
53 | 50, 52 | nfan 1828 |
. . . . . . 7
|
54 | 25, 27, 28, 30, 32, 33, 34, 35, 1, 53 | iunconnlem 21230 |
. . . . . 6
|
55 | | incom 3805 |
. . . . . . . 8
|
56 | 55, 35 | syl5eqss 3649 |
. . . . . . 7
|
57 | | uncom 3757 |
. . . . . . . 8
|
58 | 1, 57 | syl6sseq 3651 |
. . . . . . 7
|
59 | 25, 27, 28, 30, 33, 32, 2, 56, 58, 53 | iunconnlem 21230 |
. . . . . 6
|
60 | | ioran 511 |
. . . . . 6
|
61 | 54, 59, 60 | sylanbrc 698 |
. . . . 5
|
62 | 23, 61 | pm2.65da 600 |
. . . 4
|
63 | 62 | ex 450 |
. . 3
|
64 | 63 | ralrimivva 2971 |
. 2
|
65 | 26 | ralrimiva 2966 |
. . . 4
|
66 | | iunss 4561 |
. . . 4
|
67 | 65, 66 | sylibr 224 |
. . 3
|
68 | | connsub 21224 |
. . 3
TopOn
↾t Conn
|
69 | 24, 67, 68 | syl2anc 693 |
. 2
↾t
Conn
|
70 | 64, 69 | mpbird 247 |
1
↾t Conn |