Step |
Hyp |
Ref |
Expression |
1 |
|
olc |
|
2 |
|
ovex |
|
3 |
|
elprg |
|
4 |
2 3
|
mp1i |
|
5 |
1 4
|
mpbird |
|
6 |
|
2lgs |
|
7 |
6
|
ad2antlr |
|
8 |
|
2z |
|
9 |
|
simpr |
|
10 |
9
|
adantr |
|
11 |
|
2re |
|
12 |
11
|
a1i |
|
13 |
|
2m1e1 |
|
14 |
11
|
a1i |
|
15 |
|
prmnn |
|
16 |
15
|
nnred |
|
17 |
|
1lt2 |
|
18 |
17
|
a1i |
|
19 |
|
prmgt1 |
|
20 |
14 16 18 19
|
mulgt1d |
|
21 |
13 20
|
eqbrtrid |
|
22 |
|
1red |
|
23 |
|
2nn |
|
24 |
23
|
a1i |
|
25 |
24 15
|
nnmulcld |
|
26 |
25
|
nnred |
|
27 |
14 22 26
|
ltsubaddd |
|
28 |
21 27
|
mpbid |
|
29 |
28
|
ad2antrr |
|
30 |
|
breq2 |
|
31 |
30
|
adantl |
|
32 |
29 31
|
mpbird |
|
33 |
12 32
|
gtned |
|
34 |
|
eldifsn |
|
35 |
10 33 34
|
sylanbrc |
|
36 |
|
lgsqrmodndvds |
|
37 |
8 35 36
|
sylancr |
|
38 |
|
prmnn |
|
39 |
38
|
nncnd |
|
40 |
39
|
adantl |
|
41 |
|
1cnd |
|
42 |
|
2cnd |
|
43 |
15
|
nncnd |
|
44 |
42 43
|
mulcld |
|
45 |
44
|
adantr |
|
46 |
40 41 45
|
subadd2d |
|
47 |
|
prmz |
|
48 |
|
peano2zm |
|
49 |
47 48
|
syl |
|
50 |
49
|
zcnd |
|
51 |
50
|
adantl |
|
52 |
43
|
adantr |
|
53 |
|
2cnne0 |
|
54 |
53
|
a1i |
|
55 |
|
divmul2 |
|
56 |
51 52 54 55
|
syl3anc |
|
57 |
|
eqcom |
|
58 |
57
|
a1i |
|
59 |
46 56 58
|
3bitr4rd |
|
60 |
59
|
biimpa |
|
61 |
|
oveq2 |
|
62 |
|
zsqcl |
|
63 |
62
|
ad2antlr |
|
64 |
8
|
a1i |
|
65 |
|
oveq1 |
|
66 |
65
|
adantl |
|
67 |
66
|
oveq1d |
|
68 |
|
pncan1 |
|
69 |
44 68
|
syl |
|
70 |
69
|
oveq1d |
|
71 |
|
2ne0 |
|
72 |
71
|
a1i |
|
73 |
43 42 72
|
divcan3d |
|
74 |
70 73
|
eqtrd |
|
75 |
74
|
ad2antrr |
|
76 |
67 75
|
eqtrd |
|
77 |
15
|
nnnn0d |
|
78 |
77
|
ad2antrr |
|
79 |
76 78
|
eqeltrd |
|
80 |
38
|
nnrpd |
|
81 |
80
|
ad2antlr |
|
82 |
79 81
|
jca |
|
83 |
82
|
ad2antrr |
|
84 |
|
simpr |
|
85 |
|
modexp |
|
86 |
63 64 83 84 85
|
syl211anc |
|
87 |
86
|
ex |
|
88 |
87
|
adantr |
|
89 |
|
2cnd |
|
90 |
71
|
a1i |
|
91 |
50 89 90
|
divcan2d |
|
92 |
91
|
eqcomd |
|
93 |
92
|
oveq2d |
|
94 |
93
|
ad3antlr |
|
95 |
|
zcn |
|
96 |
95
|
adantl |
|
97 |
79
|
adantr |
|
98 |
|
2nn0 |
|
99 |
98
|
a1i |
|
100 |
96 97 99
|
expmuld |
|
101 |
94 100
|
eqtr2d |
|
102 |
101
|
oveq1d |
|
103 |
102
|
adantr |
|
104 |
|
vfermltl |
|
105 |
104
|
ad5ant245 |
|
106 |
103 105
|
eqtrd |
|
107 |
|
oveq1 |
|
108 |
106 107
|
eqeqan12d |
|
109 |
|
id |
|
110 |
109
|
eqcomd |
|
111 |
38
|
nnred |
|
112 |
|
prmgt1 |
|
113 |
|
1mod |
|
114 |
111 112 113
|
syl2anc |
|
115 |
114
|
eqcomd |
|
116 |
115
|
ad3antlr |
|
117 |
110 116
|
sylan9eqr |
|
118 |
38
|
ad4antlr |
|
119 |
|
zexpcl |
|
120 |
8 77 119
|
sylancr |
|
121 |
120
|
ad4antr |
|
122 |
|
1zzd |
|
123 |
|
moddvds |
|
124 |
118 121 122 123
|
syl3anc |
|
125 |
117 124
|
mpbid |
|
126 |
125
|
ex |
|
127 |
126
|
ad2antrr |
|
128 |
108 127
|
sylbid |
|
129 |
128
|
ex |
|
130 |
129
|
com23 |
|
131 |
88 130
|
syld |
|
132 |
131
|
ex |
|
133 |
132
|
com23 |
|
134 |
133
|
impd |
|
135 |
134
|
com23 |
|
136 |
135
|
ex |
|
137 |
136
|
com23 |
|
138 |
61 137
|
syl5 |
|
139 |
60 138
|
mpd |
|
140 |
139
|
rexlimdv |
|
141 |
37 140
|
syld |
|
142 |
7 141
|
sylbird |
|
143 |
5 142
|
syl5 |
|
144 |
143
|
ex |
|
145 |
144
|
com23 |
|
146 |
145
|
ex |
|
147 |
146
|
3imp2 |
|