Step | Hyp | Ref
| Expression |
1 | | simpr 109 |
. . . . . . . . 9
|
2 | | cnmptid.j |
. . . . . . . . . . . 12
TopOn |
3 | | cnmpt11.k |
. . . . . . . . . . . 12
TopOn |
4 | | cnmpt11.a |
. . . . . . . . . . . 12
|
5 | | cnf2 12752 |
. . . . . . . . . . . 12
TopOn TopOn
|
6 | 2, 3, 4, 5 | syl3anc 1227 |
. . . . . . . . . . 11
|
7 | | eqid 2164 |
. . . . . . . . . . . 12
|
8 | 7 | fmpt 5629 |
. . . . . . . . . . 11
|
9 | 6, 8 | sylibr 133 |
. . . . . . . . . 10
|
10 | 9 | r19.21bi 2552 |
. . . . . . . . 9
|
11 | 7 | fvmpt2 5563 |
. . . . . . . . 9
|
12 | 1, 10, 11 | syl2anc 409 |
. . . . . . . 8
|
13 | 12 | fveq2d 5484 |
. . . . . . 7
|
14 | | eqid 2164 |
. . . . . . . 8
|
15 | | cnmpt11.c |
. . . . . . . 8
|
16 | 15 | eleq1d 2233 |
. . . . . . . . 9
|
17 | | cnmpt11.b |
. . . . . . . . . . . . . 14
|
18 | | cntop2 12749 |
. . . . . . . . . . . . . 14
|
19 | 17, 18 | syl 14 |
. . . . . . . . . . . . 13
|
20 | | eqid 2164 |
. . . . . . . . . . . . . 14
|
21 | 20 | toptopon 12563 |
. . . . . . . . . . . . 13
TopOn |
22 | 19, 21 | sylib 121 |
. . . . . . . . . . . 12
TopOn |
23 | | cnf2 12752 |
. . . . . . . . . . . 12
TopOn TopOn |
24 | 3, 22, 17, 23 | syl3anc 1227 |
. . . . . . . . . . 11
|
25 | 14 | fmpt 5629 |
. . . . . . . . . . 11
|
26 | 24, 25 | sylibr 133 |
. . . . . . . . . 10
|
27 | 26 | adantr 274 |
. . . . . . . . 9
|
28 | 16, 27, 10 | rspcdva 2830 |
. . . . . . . 8
|
29 | 14, 15, 10, 28 | fvmptd3 5573 |
. . . . . . 7
|
30 | 13, 29 | eqtrd 2197 |
. . . . . 6
|
31 | | fvco3 5551 |
. . . . . . 7
|
32 | 6, 31 | sylan 281 |
. . . . . 6
|
33 | | eqid 2164 |
. . . . . . . 8
|
34 | 33 | fvmpt2 5563 |
. . . . . . 7
|
35 | 1, 28, 34 | syl2anc 409 |
. . . . . 6
|
36 | 30, 32, 35 | 3eqtr4d 2207 |
. . . . 5
|
37 | 36 | ralrimiva 2537 |
. . . 4
|
38 | | nfv 1515 |
. . . . 5
|
39 | | nfcv 2306 |
. . . . . . . 8
|
40 | | nfmpt1 4069 |
. . . . . . . 8
|
41 | 39, 40 | nfco 4763 |
. . . . . . 7
|
42 | | nfcv 2306 |
. . . . . . 7
|
43 | 41, 42 | nffv 5490 |
. . . . . 6
|
44 | | nfmpt1 4069 |
. . . . . . 7
|
45 | 44, 42 | nffv 5490 |
. . . . . 6
|
46 | 43, 45 | nfeq 2314 |
. . . . 5
|
47 | | fveq2 5480 |
. . . . . 6
|
48 | | fveq2 5480 |
. . . . . 6
|
49 | 47, 48 | eqeq12d 2179 |
. . . . 5
|
50 | 38, 46, 49 | cbvral 2685 |
. . . 4
|
51 | 37, 50 | sylib 121 |
. . 3
|
52 | | fco 5347 |
. . . . . 6
|
53 | 24, 6, 52 | syl2anc 409 |
. . . . 5
|
54 | 53 | ffnd 5332 |
. . . 4
|
55 | 28 | fmpttd 5634 |
. . . . 5
|
56 | 55 | ffnd 5332 |
. . . 4
|
57 | | eqfnfv 5577 |
. . . 4
|
58 | 54, 56, 57 | syl2anc 409 |
. . 3
|
59 | 51, 58 | mpbird 166 |
. 2
|
60 | | cnco 12768 |
. . 3
|
61 | 4, 17, 60 | syl2anc 409 |
. 2
|
62 | 59, 61 | eqeltrrd 2242 |
1
|