Step |
Hyp |
Ref |
Expression |
1 |
|
evennn2n |
|
2 |
1
|
3ad2ant3 |
|
3 |
|
oveq2 |
|
4 |
3
|
eqcoms |
|
5 |
|
2cnd |
|
6 |
|
nncn |
|
7 |
5 6
|
mulcomd |
|
8 |
7
|
oveq2d |
|
9 |
|
2nn0 |
|
10 |
9
|
a1i |
|
11 |
|
nnnn0 |
|
12 |
5 10 11
|
expmuld |
|
13 |
8 12
|
eqtrd |
|
14 |
13
|
adantl |
|
15 |
4 14
|
sylan9eqr |
|
16 |
15
|
oveq1d |
|
17 |
16
|
eqeq1d |
|
18 |
|
elnn1uz2 |
|
19 |
|
oveq2 |
|
20 |
|
2cn |
|
21 |
|
exp1 |
|
22 |
20 21
|
ax-mp |
|
23 |
19 22
|
eqtrdi |
|
24 |
23
|
oveq1d |
|
25 |
24
|
oveq1d |
|
26 |
|
sq2 |
|
27 |
26
|
oveq1i |
|
28 |
|
4m1e3 |
|
29 |
27 28
|
eqtri |
|
30 |
25 29
|
eqtrdi |
|
31 |
30
|
eqeq1d |
|
32 |
31
|
adantr |
|
33 |
|
eqcom |
|
34 |
|
eldifi |
|
35 |
|
prmnn |
|
36 |
|
nnre |
|
37 |
34 35 36
|
3syl |
|
38 |
37
|
3ad2ant1 |
|
39 |
|
nnnn0 |
|
40 |
39
|
3ad2ant2 |
|
41 |
38 40
|
reexpcld |
|
42 |
41
|
adantr |
|
43 |
|
simpr |
|
44 |
42 43
|
eqled |
|
45 |
44
|
ex |
|
46 |
33 45
|
syl5bi |
|
47 |
35
|
nnred |
|
48 |
|
prmgt1 |
|
49 |
47 48
|
jca |
|
50 |
34 49
|
syl |
|
51 |
50
|
3ad2ant1 |
|
52 |
|
nnz |
|
53 |
52
|
3ad2ant2 |
|
54 |
|
3rp |
|
55 |
54
|
a1i |
|
56 |
|
efexple |
|
57 |
51 53 55 56
|
syl3anc |
|
58 |
|
oddprmge3 |
|
59 |
|
eluzle |
|
60 |
58 59
|
syl |
|
61 |
54
|
a1i |
|
62 |
|
nnrp |
|
63 |
34 35 62
|
3syl |
|
64 |
61 63
|
logled |
|
65 |
60 64
|
mpbid |
|
66 |
65
|
3ad2ant1 |
|
67 |
|
relogcl |
|
68 |
54 67
|
ax-mp |
|
69 |
|
rplogcl |
|
70 |
34 49 69
|
3syl |
|
71 |
70
|
3ad2ant1 |
|
72 |
|
divle1le |
|
73 |
68 71 72
|
sylancr |
|
74 |
66 73
|
mpbird |
|
75 |
|
fldivle |
|
76 |
68 71 75
|
sylancr |
|
77 |
|
nnre |
|
78 |
77
|
3ad2ant2 |
|
79 |
68
|
a1i |
|
80 |
62
|
relogcld |
|
81 |
34 35 80
|
3syl |
|
82 |
35
|
nnrpd |
|
83 |
|
1red |
|
84 |
83 48
|
gtned |
|
85 |
82 84
|
jca |
|
86 |
|
logne0 |
|
87 |
34 85 86
|
3syl |
|
88 |
79 81 87
|
redivcld |
|
89 |
88
|
flcld |
|
90 |
89
|
zred |
|
91 |
90
|
3ad2ant1 |
|
92 |
88
|
3ad2ant1 |
|
93 |
|
letr |
|
94 |
78 91 92 93
|
syl3anc |
|
95 |
|
1red |
|
96 |
|
letr |
|
97 |
78 92 95 96
|
syl3anc |
|
98 |
|
nnge1 |
|
99 |
|
eqcom |
|
100 |
|
1red |
|
101 |
100 77
|
letri3d |
|
102 |
99 101
|
syl5rbb |
|
103 |
102
|
biimpd |
|
104 |
98 103
|
mpand |
|
105 |
104
|
3ad2ant2 |
|
106 |
97 105
|
syld |
|
107 |
106
|
expd |
|
108 |
94 107
|
syld |
|
109 |
76 108
|
mpan2d |
|
110 |
74 109
|
mpid |
|
111 |
57 110
|
sylbid |
|
112 |
46 111
|
syld |
|
113 |
112
|
adantl |
|
114 |
32 113
|
sylbid |
|
115 |
114
|
ex |
|
116 |
|
sq1 |
|
117 |
116
|
eqcomi |
|
118 |
117
|
oveq2i |
|
119 |
118
|
eqeq1i |
|
120 |
|
eqcom |
|
121 |
9
|
a1i |
|
122 |
|
eluzge2nn0 |
|
123 |
121 122
|
nn0expcld |
|
124 |
123
|
adantr |
|
125 |
|
1nn0 |
|
126 |
125
|
a1i |
|
127 |
|
1p1e2 |
|
128 |
22
|
eqcomi |
|
129 |
127 128
|
eqtri |
|
130 |
|
eluz2gt1 |
|
131 |
|
2re |
|
132 |
131
|
a1i |
|
133 |
|
1zzd |
|
134 |
|
eluzelz |
|
135 |
|
1lt2 |
|
136 |
135
|
a1i |
|
137 |
132 133 134 136
|
ltexp2d |
|
138 |
130 137
|
mpbid |
|
139 |
129 138
|
eqbrtrid |
|
140 |
139
|
adantr |
|
141 |
34 39
|
anim12i |
|
142 |
141
|
3adant3 |
|
143 |
142
|
adantl |
|
144 |
|
difsqpwdvds |
|
145 |
124 126 140 143 144
|
syl31anc |
|
146 |
|
2t1e2 |
|
147 |
146
|
breq2i |
|
148 |
|
prmuz2 |
|
149 |
34 148
|
syl |
|
150 |
|
2prm |
|
151 |
|
dvdsprm |
|
152 |
149 150 151
|
sylancl |
|
153 |
147 152
|
syl5bb |
|
154 |
|
eldifsn |
|
155 |
|
eqneqall |
|
156 |
155
|
com12 |
|
157 |
154 156
|
simplbiim |
|
158 |
153 157
|
sylbid |
|
159 |
158
|
3ad2ant1 |
|
160 |
159
|
adantl |
|
161 |
145 160
|
syld |
|
162 |
120 161
|
syl5bi |
|
163 |
119 162
|
syl5bi |
|
164 |
163
|
ex |
|
165 |
115 164
|
jaoi |
|
166 |
18 165
|
sylbi |
|
167 |
166
|
impcom |
|
168 |
167
|
adantr |
|
169 |
17 168
|
sylbid |
|
170 |
169
|
rexlimdva2 |
|
171 |
2 170
|
sylbid |
|
172 |
171
|
3imp |
|