Step |
Hyp |
Ref |
Expression |
1 |
|
jm2.27a1 |
|
2 |
|
jm2.27a2 |
|
3 |
|
jm2.27a3 |
|
4 |
|
jm2.27a4 |
|
5 |
|
jm2.27a5 |
|
6 |
|
jm2.27a6 |
|
7 |
|
jm2.27a7 |
|
8 |
|
jm2.27a8 |
|
9 |
|
jm2.27a9 |
|
10 |
|
jm2.27a10 |
|
11 |
|
jm2.27a11 |
|
12 |
|
jm2.27a12 |
|
13 |
|
jm2.27a13 |
|
14 |
|
jm2.27a14 |
|
15 |
|
jm2.27a15 |
|
16 |
|
jm2.27a16 |
|
17 |
|
jm2.27a17 |
|
18 |
|
jm2.27a18 |
|
19 |
|
jm2.27a19 |
|
20 |
|
jm2.27a20 |
|
21 |
|
jm2.27a21 |
|
22 |
|
jm2.27a22 |
|
23 |
|
jm2.27a23 |
|
24 |
|
jm2.27a24 |
|
25 |
|
jm2.27a25 |
|
26 |
|
jm2.27a26 |
|
27 |
|
jm2.27a27 |
|
28 |
|
jm2.27a28 |
|
29 |
|
jm2.27a29 |
|
30 |
|
2z |
|
31 |
3
|
nnzd |
|
32 |
|
zmulcl |
|
33 |
30 31 32
|
sylancr |
|
34 |
2
|
nnzd |
|
35 |
8
|
nn0zd |
|
36 |
|
congsym |
|
37 |
33 35 34 19 36
|
syl22anc |
|
38 |
7
|
nn0zd |
|
39 |
|
peano2zm |
|
40 |
38 39
|
syl |
|
41 |
35 27
|
zsubcld |
|
42 |
8
|
nn0ge0d |
|
43 |
|
rmy0 |
|
44 |
13 43
|
syl |
|
45 |
29
|
eqcomd |
|
46 |
42 44 45
|
3brtr4d |
|
47 |
|
0zd |
|
48 |
|
lermy |
|
49 |
13 47 27 48
|
syl3anc |
|
50 |
46 49
|
mpbird |
|
51 |
|
elnn0z |
|
52 |
27 50 51
|
sylanbrc |
|
53 |
|
jm2.16nn0 |
|
54 |
13 52 53
|
syl2anc |
|
55 |
29
|
oveq1d |
|
56 |
54 55
|
breqtrrd |
|
57 |
33 40 41 17 56
|
dvdstrd |
|
58 |
|
congtr |
|
59 |
33 34 35 27 37 57 58
|
syl222anc |
|
60 |
59
|
orcd |
|
61 |
|
zmulcl |
|
62 |
30 24 61
|
sylancr |
|
63 |
|
zsqcl |
|
64 |
31 63
|
syl |
|
65 |
|
dvdsmul2 |
|
66 |
30 64 65
|
sylancr |
|
67 |
10
|
nn0zd |
|
68 |
67
|
peano2zd |
|
69 |
|
zmulcl |
|
70 |
30 64 69
|
sylancr |
|
71 |
|
dvdsmultr2 |
|
72 |
64 68 70 71
|
syl3anc |
|
73 |
66 72
|
mpd |
|
74 |
23
|
oveq1d |
|
75 |
15 26
|
eqtr3d |
|
76 |
73 74 75
|
3brtr3d |
|
77 |
68
|
zred |
|
78 |
70
|
zred |
|
79 |
|
nn0p1nn |
|
80 |
10 79
|
syl |
|
81 |
80
|
nngt0d |
|
82 |
|
2nn |
|
83 |
3
|
nnsqcld |
|
84 |
|
nnmulcl |
|
85 |
82 83 84
|
sylancr |
|
86 |
85
|
nngt0d |
|
87 |
77 78 81 86
|
mulgt0d |
|
88 |
87 15
|
breqtrrd |
|
89 |
|
rmy0 |
|
90 |
1 89
|
syl |
|
91 |
26
|
eqcomd |
|
92 |
88 90 91
|
3brtr4d |
|
93 |
|
ltrmy |
|
94 |
1 47 24 93
|
syl3anc |
|
95 |
92 94
|
mpbird |
|
96 |
|
elnnz |
|
97 |
24 95 96
|
sylanbrc |
|
98 |
3
|
nngt0d |
|
99 |
23
|
eqcomd |
|
100 |
98 90 99
|
3brtr4d |
|
101 |
|
ltrmy |
|
102 |
1 47 21 101
|
syl3anc |
|
103 |
100 102
|
mpbird |
|
104 |
|
elnnz |
|
105 |
21 103 104
|
sylanbrc |
|
106 |
|
jm2.20nn |
|
107 |
1 97 105 106
|
syl3anc |
|
108 |
76 107
|
mpbid |
|
109 |
23 31
|
eqeltrrd |
|
110 |
|
muldvds2 |
|
111 |
21 109 24 110
|
syl3anc |
|
112 |
108 111
|
mpd |
|
113 |
23 112
|
eqbrtrd |
|
114 |
30
|
a1i |
|
115 |
|
dvdscmul |
|
116 |
31 24 114 115
|
syl3anc |
|
117 |
113 116
|
mpd |
|
118 |
6
|
nn0zd |
|
119 |
25 118
|
eqeltrrd |
|
120 |
|
frmy |
|
121 |
120
|
fovcl |
|
122 |
1 27 121
|
syl2anc |
|
123 |
29 35
|
eqeltrrd |
|
124 |
|
eluzelz |
|
125 |
1 124
|
syl |
|
126 |
125 38
|
zsubcld |
|
127 |
122 123
|
zsubcld |
|
128 |
|
congsym |
|
129 |
118 38 125 16 128
|
syl22anc |
|
130 |
25 129
|
eqbrtrrd |
|
131 |
|
jm2.15nn0 |
|
132 |
1 13 52 131
|
syl3anc |
|
133 |
119 126 127 130 132
|
dvdstrd |
|
134 |
29 23
|
oveq12d |
|
135 |
18 25 134
|
3brtr3d |
|
136 |
|
congtr |
|
137 |
119 122 123 109 133 135 136
|
syl222anc |
|
138 |
137
|
orcd |
|
139 |
|
jm2.26 |
|
140 |
1 97 27 21 139
|
syl22anc |
|
141 |
138 140
|
mpbid |
|
142 |
|
dvdsacongtr |
|
143 |
62 27 21 33 117 141 142
|
syl222anc |
|
144 |
|
acongtr |
|
145 |
33 34 27 21 60 143 144
|
syl222anc |
|
146 |
2
|
nnnn0d |
|
147 |
3
|
nnnn0d |
|
148 |
|
elfz2nn0 |
|
149 |
146 147 20 148
|
syl3anbrc |
|
150 |
105
|
nnnn0d |
|
151 |
|
rmygeid |
|
152 |
1 150 151
|
syl2anc |
|
153 |
152 23
|
breqtrrd |
|
154 |
|
elfz2nn0 |
|
155 |
150 147 153 154
|
syl3anbrc |
|
156 |
|
acongeq |
|
157 |
3 149 155 156
|
syl3anc |
|
158 |
145 157
|
mpbird |
|
159 |
158
|
oveq2d |
|
160 |
23 159
|
eqtr4d |
|