Step |
Hyp |
Ref |
Expression |
1 |
|
fprodsplit.1 |
|
2 |
|
fprodsplit.2 |
|
3 |
|
fprodsplit.3 |
|
4 |
|
fprodsplit.4 |
|
5 |
|
iftrue |
|
6 |
5
|
prodeq2i |
|
7 |
|
ssun1 |
|
8 |
7 2
|
sseqtrrid |
|
9 |
5
|
adantl |
|
10 |
8
|
sselda |
|
11 |
10 4
|
syldan |
|
12 |
9 11
|
eqeltrd |
|
13 |
|
eldifn |
|
14 |
13
|
iffalsed |
|
15 |
14
|
adantl |
|
16 |
8 12 15 3
|
fprodss |
|
17 |
6 16
|
syl5eqr |
|
18 |
|
iftrue |
|
19 |
18
|
prodeq2i |
|
20 |
|
ssun2 |
|
21 |
20 2
|
sseqtrrid |
|
22 |
18
|
adantl |
|
23 |
21
|
sselda |
|
24 |
23 4
|
syldan |
|
25 |
22 24
|
eqeltrd |
|
26 |
|
eldifn |
|
27 |
26
|
iffalsed |
|
28 |
27
|
adantl |
|
29 |
21 25 28 3
|
fprodss |
|
30 |
19 29
|
syl5eqr |
|
31 |
17 30
|
oveq12d |
|
32 |
|
ax-1cn |
|
33 |
|
ifcl |
|
34 |
4 32 33
|
sylancl |
|
35 |
|
ifcl |
|
36 |
4 32 35
|
sylancl |
|
37 |
3 34 36
|
fprodmul |
|
38 |
2
|
eleq2d |
|
39 |
|
elun |
|
40 |
38 39
|
bitrdi |
|
41 |
40
|
biimpa |
|
42 |
|
disjel |
|
43 |
1 42
|
sylan |
|
44 |
43
|
iffalsed |
|
45 |
9 44
|
oveq12d |
|
46 |
11
|
mulid1d |
|
47 |
45 46
|
eqtrd |
|
48 |
43
|
ex |
|
49 |
48
|
con2d |
|
50 |
49
|
imp |
|
51 |
50
|
iffalsed |
|
52 |
51 22
|
oveq12d |
|
53 |
24
|
mulid2d |
|
54 |
52 53
|
eqtrd |
|
55 |
47 54
|
jaodan |
|
56 |
41 55
|
syldan |
|
57 |
56
|
prodeq2dv |
|
58 |
31 37 57
|
3eqtr2rd |
|