Step | Hyp | Ref
| Expression |
1 | | nffvmpt1 6199 |
. . . . 5
|
2 | | nfcv 2764 |
. . . . 5
|
3 | 1, 2 | nffv 6198 |
. . . 4
|
4 | | nfcv 2764 |
. . . . . . 7
|
5 | | nfmpt1 4747 |
. . . . . . 7
|
6 | 4, 5 | nfmpt 4746 |
. . . . . 6
|
7 | | nfcv 2764 |
. . . . . 6
|
8 | 6, 7 | nffv 6198 |
. . . . 5
|
9 | | nfcv 2764 |
. . . . 5
|
10 | 8, 9 | nffv 6198 |
. . . 4
|
11 | | nfcv 2764 |
. . . 4
|
12 | | nfcv 2764 |
. . . 4
|
13 | | fveq2 6191 |
. . . . . 6
|
14 | 13 | fveq1d 6193 |
. . . . 5
|
15 | | fveq2 6191 |
. . . . 5
|
16 | 14, 15 | sylan9eq 2676 |
. . . 4
|
17 | 3, 10, 11, 12, 16 | cbvmpt2 6734 |
. . 3
|
18 | | simplr 792 |
. . . . . . . 8
|
19 | | cnmptk1p.j |
. . . . . . . . . . . 12
TopOn |
20 | | cnmptk1p.n |
. . . . . . . . . . . . . 14
𝑛Locally |
21 | | nllytop 21276 |
. . . . . . . . . . . . . 14
𝑛Locally |
22 | 20, 21 | syl 17 |
. . . . . . . . . . . . 13
|
23 | | cnmptk1p.l |
. . . . . . . . . . . . . 14
TopOn |
24 | | topontop 20718 |
. . . . . . . . . . . . . 14
TopOn
|
25 | 23, 24 | syl 17 |
. . . . . . . . . . . . 13
|
26 | | eqid 2622 |
. . . . . . . . . . . . . 14
|
27 | 26 | xkotopon 21403 |
. . . . . . . . . . . . 13
TopOn |
28 | 22, 25, 27 | syl2anc 693 |
. . . . . . . . . . . 12
TopOn |
29 | | cnmptk2.a |
. . . . . . . . . . . 12
|
30 | | cnf2 21053 |
. . . . . . . . . . . 12
TopOn TopOn
|
31 | 19, 28, 29, 30 | syl3anc 1326 |
. . . . . . . . . . 11
|
32 | | eqid 2622 |
. . . . . . . . . . . 12
|
33 | 32 | fmpt 6381 |
. . . . . . . . . . 11
|
34 | 31, 33 | sylibr 224 |
. . . . . . . . . 10
|
35 | 34 | r19.21bi 2932 |
. . . . . . . . 9
|
36 | 35 | adantr 481 |
. . . . . . . 8
|
37 | 32 | fvmpt2 6291 |
. . . . . . . 8
|
38 | 18, 36, 37 | syl2anc 693 |
. . . . . . 7
|
39 | 38 | fveq1d 6193 |
. . . . . 6
|
40 | | simpr 477 |
. . . . . . 7
|
41 | | cnmptk1p.k |
. . . . . . . . . . 11
TopOn |
42 | 41 | adantr 481 |
. . . . . . . . . 10
TopOn |
43 | 23 | adantr 481 |
. . . . . . . . . 10
TopOn |
44 | | cnf2 21053 |
. . . . . . . . . 10
TopOn TopOn
|
45 | 42, 43, 35, 44 | syl3anc 1326 |
. . . . . . . . 9
|
46 | | eqid 2622 |
. . . . . . . . . 10
|
47 | 46 | fmpt 6381 |
. . . . . . . . 9
|
48 | 45, 47 | sylibr 224 |
. . . . . . . 8
|
49 | 48 | r19.21bi 2932 |
. . . . . . 7
|
50 | 46 | fvmpt2 6291 |
. . . . . . 7
|
51 | 40, 49, 50 | syl2anc 693 |
. . . . . 6
|
52 | 39, 51 | eqtrd 2656 |
. . . . 5
|
53 | 52 | 3impa 1259 |
. . . 4
|
54 | 53 | mpt2eq3dva 6719 |
. . 3
|
55 | 17, 54 | syl5eq 2668 |
. 2
|
56 | 19, 41 | cnmpt1st 21471 |
. . . 4
|
57 | 19, 41, 56, 29 | cnmpt21f 21475 |
. . 3
|
58 | 19, 41 | cnmpt2nd 21472 |
. . 3
|
59 | | eqid 2622 |
. . . . 5
|
60 | | toponuni 20719 |
. . . . . 6
TopOn
|
61 | 41, 60 | syl 17 |
. . . . 5
|
62 | | mpt2eq12 6715 |
. . . . 5
|
63 | 59, 61, 62 | sylancr 695 |
. . . 4
|
64 | | eqid 2622 |
. . . . . 6
|
65 | | eqid 2622 |
. . . . . 6
|
66 | 64, 65 | xkofvcn 21487 |
. . . . 5
𝑛Locally
|
67 | 20, 25, 66 | syl2anc 693 |
. . . 4
|
68 | 63, 67 | eqeltrd 2701 |
. . 3
|
69 | | fveq1 6190 |
. . . 4
|
70 | | fveq2 6191 |
. . . 4
|
71 | 69, 70 | sylan9eq 2676 |
. . 3
|
72 | 19, 41, 57, 58, 28, 41, 68, 71 | cnmpt22 21477 |
. 2
|
73 | 55, 72 | eqeltrrd 2702 |
1
|