Step |
Hyp |
Ref |
Expression |
1 |
|
fveq2 |
|
2 |
1
|
neeq1d |
|
3 |
|
breq1 |
|
4 |
2 3
|
anbi12d |
|
5 |
4
|
elrab |
|
6 |
|
muval2 |
|
7 |
6
|
adantrr |
|
8 |
5 7
|
sylbi |
|
9 |
8
|
adantl |
|
10 |
9
|
sumeq2dv |
|
11 |
|
simpr |
|
12 |
11
|
a1i |
|
13 |
12
|
ss2rabdv |
|
14 |
|
ssrab2 |
|
15 |
|
simpr |
|
16 |
14 15
|
sseldi |
|
17 |
|
mucl |
|
18 |
16 17
|
syl |
|
19 |
18
|
zcnd |
|
20 |
|
difrab |
|
21 |
|
pm3.21 |
|
22 |
21
|
necon1bd |
|
23 |
22
|
imp |
|
24 |
23
|
a1i |
|
25 |
24
|
ss2rabi |
|
26 |
20 25
|
eqsstri |
|
27 |
26
|
sseli |
|
28 |
|
fveqeq2 |
|
29 |
28
|
elrab |
|
30 |
29
|
simprbi |
|
31 |
27 30
|
syl |
|
32 |
31
|
adantl |
|
33 |
|
fzfid |
|
34 |
|
dvdsssfz1 |
|
35 |
33 34
|
ssfid |
|
36 |
13 19 32 35
|
fsumss |
|
37 |
|
fveq2 |
|
38 |
37
|
oveq2d |
|
39 |
35 13
|
ssfid |
|
40 |
|
eqid |
|
41 |
|
eqid |
|
42 |
|
oveq1 |
|
43 |
42
|
cbvmptv |
|
44 |
|
oveq2 |
|
45 |
44
|
mpteq2dv |
|
46 |
43 45
|
syl5eq |
|
47 |
46
|
cbvmptv |
|
48 |
40 41 47
|
sqff1o |
|
49 |
|
breq2 |
|
50 |
49
|
rabbidv |
|
51 |
|
prmex |
|
52 |
51
|
rabex |
|
53 |
50 41 52
|
fvmpt |
|
54 |
53
|
adantl |
|
55 |
|
neg1cn |
|
56 |
|
prmdvdsfi |
|
57 |
|
elpwi |
|
58 |
|
ssfi |
|
59 |
56 57 58
|
syl2an |
|
60 |
|
hashcl |
|
61 |
59 60
|
syl |
|
62 |
|
expcl |
|
63 |
55 61 62
|
sylancr |
|
64 |
38 39 48 54 63
|
fsumf1o |
|
65 |
|
fzfid |
|
66 |
56
|
adantr |
|
67 |
|
pwfi |
|
68 |
66 67
|
sylib |
|
69 |
|
ssrab2 |
|
70 |
|
ssfi |
|
71 |
68 69 70
|
sylancl |
|
72 |
|
simprr |
|
73 |
|
fveqeq2 |
|
74 |
73
|
elrab |
|
75 |
74
|
simprbi |
|
76 |
72 75
|
syl |
|
77 |
76
|
ralrimivva |
|
78 |
|
invdisj |
|
79 |
77 78
|
syl |
|
80 |
56
|
adantr |
|
81 |
69 72
|
sseldi |
|
82 |
81 57
|
syl |
|
83 |
80 82
|
ssfid |
|
84 |
83 60
|
syl |
|
85 |
55 84 62
|
sylancr |
|
86 |
65 71 79 85
|
fsumiun |
|
87 |
|
iunrab |
|
88 |
56
|
adantr |
|
89 |
|
elpwi |
|
90 |
89
|
adantl |
|
91 |
|
ssdomg |
|
92 |
88 90 91
|
sylc |
|
93 |
|
ssfi |
|
94 |
56 89 93
|
syl2an |
|
95 |
|
hashdom |
|
96 |
94 88 95
|
syl2anc |
|
97 |
92 96
|
mpbird |
|
98 |
|
hashcl |
|
99 |
94 98
|
syl |
|
100 |
|
nn0uz |
|
101 |
99 100
|
eleqtrdi |
|
102 |
|
hashcl |
|
103 |
56 102
|
syl |
|
104 |
103
|
adantr |
|
105 |
104
|
nn0zd |
|
106 |
|
elfz5 |
|
107 |
101 105 106
|
syl2anc |
|
108 |
97 107
|
mpbird |
|
109 |
|
eqidd |
|
110 |
|
eqeq2 |
|
111 |
110
|
rspcev |
|
112 |
108 109 111
|
syl2anc |
|
113 |
112
|
ralrimiva |
|
114 |
|
rabid2 |
|
115 |
113 114
|
sylibr |
|
116 |
87 115
|
eqtr4id |
|
117 |
116
|
sumeq1d |
|
118 |
|
elfznn0 |
|
119 |
118
|
adantl |
|
120 |
|
expcl |
|
121 |
55 119 120
|
sylancr |
|
122 |
|
fsumconst |
|
123 |
71 121 122
|
syl2anc |
|
124 |
75
|
adantl |
|
125 |
124
|
oveq2d |
|
126 |
125
|
sumeq2dv |
|
127 |
|
elfzelz |
|
128 |
|
hashbc |
|
129 |
56 127 128
|
syl2an |
|
130 |
129
|
oveq1d |
|
131 |
123 126 130
|
3eqtr4d |
|
132 |
131
|
sumeq2dv |
|
133 |
|
1pneg1e0 |
|
134 |
133
|
oveq1i |
|
135 |
|
binom1p |
|
136 |
55 103 135
|
sylancr |
|
137 |
134 136
|
syl5eqr |
|
138 |
|
eqeq2 |
|
139 |
|
eqeq2 |
|
140 |
|
nprmdvds1 |
|
141 |
|
simpr |
|
142 |
141
|
breq2d |
|
143 |
142
|
notbid |
|
144 |
140 143
|
syl5ibr |
|
145 |
144
|
ralrimiv |
|
146 |
|
rabeq0 |
|
147 |
145 146
|
sylibr |
|
148 |
147
|
fveq2d |
|
149 |
|
hash0 |
|
150 |
148 149
|
eqtrdi |
|
151 |
150
|
oveq2d |
|
152 |
|
0exp0e1 |
|
153 |
151 152
|
eqtrdi |
|
154 |
|
df-ne |
|
155 |
|
eluz2b3 |
|
156 |
155
|
biimpri |
|
157 |
154 156
|
sylan2br |
|
158 |
|
exprmfct |
|
159 |
157 158
|
syl |
|
160 |
|
rabn0 |
|
161 |
159 160
|
sylibr |
|
162 |
56
|
adantr |
|
163 |
|
hashnncl |
|
164 |
162 163
|
syl |
|
165 |
161 164
|
mpbird |
|
166 |
165
|
0expd |
|
167 |
138 139 153 166
|
ifbothda |
|
168 |
132 137 167
|
3eqtr2d |
|
169 |
86 117 168
|
3eqtr3d |
|
170 |
64 169
|
eqtr3d |
|
171 |
10 36 170
|
3eqtr3d |
|