Step |
Hyp |
Ref |
Expression |
1 |
|
etransclem28.p |
|
2 |
|
etransclem28.m |
|
3 |
|
etransclem28.n |
|
4 |
|
etransclem28.c |
|
5 |
|
etransclem28.d |
|
6 |
|
etransclem28.j |
|
7 |
|
etransclem28.t |
|
8 |
|
nnm1nn0 |
|
9 |
1 8
|
syl |
|
10 |
9
|
faccld |
|
11 |
10
|
nnzd |
|
12 |
11
|
adantr |
|
13 |
4 3
|
etransclem12 |
|
14 |
5 13
|
eleqtrd |
|
15 |
|
fveq1 |
|
16 |
15
|
sumeq2sdv |
|
17 |
16
|
eqeq1d |
|
18 |
17
|
elrab |
|
19 |
18
|
simprbi |
|
20 |
14 19
|
syl |
|
21 |
20
|
eqcomd |
|
22 |
21
|
fveq2d |
|
23 |
22
|
oveq1d |
|
24 |
|
nfcv |
|
25 |
|
fzfid |
|
26 |
|
nn0ex |
|
27 |
|
fzssnn0 |
|
28 |
27
|
a1i |
|
29 |
|
mapss |
|
30 |
26 28 29
|
sylancr |
|
31 |
|
elrabi |
|
32 |
30 31
|
sseldd |
|
33 |
14 32
|
syl |
|
34 |
24 25 33
|
mccl |
|
35 |
23 34
|
eqeltrd |
|
36 |
35
|
nnzd |
|
37 |
36
|
adantr |
|
38 |
|
df-neg |
|
39 |
|
oveq1 |
|
40 |
38 39
|
eqtr4id |
|
41 |
40
|
oveq1d |
|
42 |
41
|
oveq2d |
|
43 |
42
|
ifeq2d |
|
44 |
43
|
prodeq2ad |
|
45 |
44
|
adantl |
|
46 |
14 31
|
syl |
|
47 |
|
elmapi |
|
48 |
46 47
|
syl |
|
49 |
1 48 6
|
etransclem7 |
|
50 |
49
|
adantr |
|
51 |
45 50
|
eqeltrd |
|
52 |
12 51
|
zmulcld |
|
53 |
12 37 52
|
3jca |
|
54 |
|
dvdsmul1 |
|
55 |
12 51 54
|
syl2anc |
|
56 |
|
dvdsmultr2 |
|
57 |
53 55 56
|
sylc |
|
58 |
57
|
adantr |
|
59 |
1
|
ad2antrr |
|
60 |
2
|
ad2antrr |
|
61 |
48
|
ad2antrr |
|
62 |
|
eqid |
|
63 |
|
simplr |
|
64 |
|
simpr |
|
65 |
59 60 61 62 63 64
|
etransclem14 |
|
66 |
58 65
|
breqtrrd |
|
67 |
|
dvds0 |
|
68 |
11 67
|
syl |
|
69 |
68
|
ad2antrr |
|
70 |
1
|
ad2antrr |
|
71 |
2
|
ad2antrr |
|
72 |
3
|
ad2antrr |
|
73 |
48
|
ad2antrr |
|
74 |
|
simplr |
|
75 |
|
neqne |
|
76 |
75
|
adantl |
|
77 |
70 71 72 73 62 74 76
|
etransclem15 |
|
78 |
69 77
|
breqtrrd |
|
79 |
66 78
|
pm2.61dan |
|
80 |
1
|
nnzd |
|
81 |
|
elfznn0 |
|
82 |
6 81
|
syl |
|
83 |
82
|
nn0zd |
|
84 |
1 2 3 83 4 5
|
etransclem26 |
|
85 |
11 80 84
|
3jca |
|
86 |
85
|
adantr |
|
87 |
1
|
nncnd |
|
88 |
|
1cnd |
|
89 |
87 88
|
npcand |
|
90 |
89
|
eqcomd |
|
91 |
90
|
fveq2d |
|
92 |
|
facp1 |
|
93 |
9 92
|
syl |
|
94 |
89
|
oveq2d |
|
95 |
91 93 94
|
3eqtrrd |
|
96 |
95
|
adantr |
|
97 |
1
|
adantr |
|
98 |
2
|
adantr |
|
99 |
3
|
adantr |
|
100 |
48
|
adantr |
|
101 |
20
|
adantr |
|
102 |
|
1zzd |
|
103 |
2
|
nn0zd |
|
104 |
103
|
adantr |
|
105 |
83
|
adantr |
|
106 |
102 104 105
|
3jca |
|
107 |
82
|
adantr |
|
108 |
|
neqne |
|
109 |
108
|
adantl |
|
110 |
|
elnnne0 |
|
111 |
107 109 110
|
sylanbrc |
|
112 |
111
|
nnge1d |
|
113 |
|
elfzle2 |
|
114 |
6 113
|
syl |
|
115 |
114
|
adantr |
|
116 |
106 112 115
|
jca32 |
|
117 |
|
elfz2 |
|
118 |
116 117
|
sylibr |
|
119 |
97 98 99 100 101 62 118
|
etransclem25 |
|
120 |
96 119
|
eqbrtrd |
|
121 |
|
muldvds1 |
|
122 |
86 120 121
|
sylc |
|
123 |
79 122
|
pm2.61dan |
|
124 |
123 7
|
breqtrrdi |
|