Step |
Hyp |
Ref |
Expression |
1 |
|
fprodcnlem.1 |
|
2 |
|
fprodcnlem.k |
|
3 |
|
fprodcnlem.j |
|
4 |
|
fprodcnlem.a |
|
5 |
|
fprodcnlem.b |
|
6 |
|
fprodcnlem.z |
|
7 |
|
fprodcnlem.w |
|
8 |
|
fprodcnlem.p |
|
9 |
|
nfv |
|
10 |
1 9
|
nfan |
|
11 |
|
nfcsb1v |
|
12 |
4 6
|
ssfid |
|
13 |
12
|
adantr |
|
14 |
7
|
adantr |
|
15 |
14
|
eldifbd |
|
16 |
6
|
sselda |
|
17 |
16
|
adantlr |
|
18 |
3
|
adantr |
|
19 |
2
|
cnfldtopon |
|
20 |
19
|
a1i |
|
21 |
|
cnf2 |
|
22 |
18 20 5 21
|
syl3anc |
|
23 |
|
eqid |
|
24 |
23
|
fmpt |
|
25 |
22 24
|
sylibr |
|
26 |
25
|
adantlr |
|
27 |
|
simplr |
|
28 |
|
rspa |
|
29 |
26 27 28
|
syl2anc |
|
30 |
17 29
|
syldan |
|
31 |
|
csbeq1a |
|
32 |
14
|
eldifad |
|
33 |
|
nfv |
|
34 |
10 33
|
nfan |
|
35 |
11
|
nfel1 |
|
36 |
34 35
|
nfim |
|
37 |
|
eleq1 |
|
38 |
37
|
anbi2d |
|
39 |
31
|
eleq1d |
|
40 |
38 39
|
imbi12d |
|
41 |
36 40 29
|
vtoclg1f |
|
42 |
41
|
anabsi7 |
|
43 |
32 42
|
mpdan |
|
44 |
10 11 13 14 15 30 31 43
|
fprodsplitsn |
|
45 |
44
|
mpteq2dva |
|
46 |
7
|
eldifad |
|
47 |
1 33
|
nfan |
|
48 |
|
nfcv |
|
49 |
48 11
|
nfmpt |
|
50 |
49
|
nfel1 |
|
51 |
47 50
|
nfim |
|
52 |
37
|
anbi2d |
|
53 |
31
|
mpteq2dv |
|
54 |
53
|
eleq1d |
|
55 |
52 54
|
imbi12d |
|
56 |
51 55 5
|
vtoclg1f |
|
57 |
56
|
anabsi7 |
|
58 |
46 57
|
mpdan |
|
59 |
19
|
a1i |
|
60 |
2
|
mpomulcn |
|
61 |
60
|
a1i |
|
62 |
|
oveq12 |
|
63 |
3 8 58 59 59 61 62
|
cnmpt12 |
|
64 |
45 63
|
eqeltrd |
|