Step |
Hyp |
Ref |
Expression |
1 |
|
etransclem41.m |
|
2 |
|
etransclem41.p |
|
3 |
|
etransclem41.mp |
|
4 |
|
etransclem41.f |
|
5 |
1
|
faccld |
|
6 |
5
|
nnred |
|
7 |
|
prmnn |
|
8 |
2 7
|
syl |
|
9 |
8
|
nnred |
|
10 |
6 9
|
ltnled |
|
11 |
3 10
|
mpbid |
|
12 |
8
|
nnzd |
|
13 |
12 5
|
jca |
|
14 |
13
|
adantr |
|
15 |
|
simpr |
|
16 |
|
dvdsle |
|
17 |
14 15 16
|
sylc |
|
18 |
11 17
|
mtand |
|
19 |
|
fzfid |
|
20 |
|
elfzelz |
|
21 |
20
|
znegcld |
|
22 |
21
|
zcnd |
|
23 |
22
|
adantl |
|
24 |
19 23
|
fprodabs2 |
|
25 |
24
|
mptru |
|
26 |
20
|
zcnd |
|
27 |
26
|
absnegd |
|
28 |
20
|
zred |
|
29 |
|
0red |
|
30 |
|
1red |
|
31 |
|
0lt1 |
|
32 |
31
|
a1i |
|
33 |
|
elfzle1 |
|
34 |
29 30 28 32 33
|
ltletrd |
|
35 |
29 28 34
|
ltled |
|
36 |
28 35
|
absidd |
|
37 |
27 36
|
eqtrd |
|
38 |
37
|
prodeq2i |
|
39 |
25 38
|
eqtri |
|
40 |
|
fprodfac |
|
41 |
1 40
|
syl |
|
42 |
39 41
|
eqtr4id |
|
43 |
42
|
breq2d |
|
44 |
18 43
|
mtbird |
|
45 |
|
fzfid |
|
46 |
21
|
adantl |
|
47 |
45 46
|
fprodzcl |
|
48 |
|
dvdsabsb |
|
49 |
12 47 48
|
syl2anc |
|
50 |
44 49
|
mtbird |
|
51 |
|
prmdvdsexp |
|
52 |
2 47 8 51
|
syl3anc |
|
53 |
50 52
|
mtbird |
|
54 |
|
etransclem11 |
|
55 |
|
eqeq1 |
|
56 |
55
|
ifbid |
|
57 |
56
|
cbvmptv |
|
58 |
8 1 4 54 57
|
etransclem35 |
|
59 |
58
|
oveq1d |
|
60 |
22
|
adantl |
|
61 |
45 60
|
fprodcl |
|
62 |
8
|
nnnn0d |
|
63 |
61 62
|
expcld |
|
64 |
|
nnm1nn0 |
|
65 |
8 64
|
syl |
|
66 |
65
|
faccld |
|
67 |
66
|
nncnd |
|
68 |
66
|
nnne0d |
|
69 |
63 67 68
|
divcan3d |
|
70 |
59 69
|
eqtrd |
|
71 |
70
|
breq2d |
|
72 |
53 71
|
mtbird |
|