Step |
Hyp |
Ref |
Expression |
1 |
|
gexcl.1 |
|
2 |
|
gexcl.2 |
|
3 |
|
gexid.3 |
|
4 |
|
gexid.4 |
|
5 |
1 2 3 4
|
gexdvdsi |
|
6 |
5
|
3expia |
|
7 |
6
|
ralrimdva |
|
8 |
7
|
adantr |
|
9 |
|
noel |
|
10 |
|
simprr |
|
11 |
10
|
eleq2d |
|
12 |
|
oveq1 |
|
13 |
12
|
eqeq1d |
|
14 |
13
|
ralbidv |
|
15 |
14
|
elrab |
|
16 |
11 15
|
bitr3di |
|
17 |
16
|
rbaibd |
|
18 |
9 17
|
mtbii |
|
19 |
18
|
ex |
|
20 |
|
nn0abscl |
|
21 |
20
|
ad2antlr |
|
22 |
|
elnn0 |
|
23 |
21 22
|
sylib |
|
24 |
23
|
ord |
|
25 |
19 24
|
syld |
|
26 |
|
simpr |
|
27 |
26
|
oveq1d |
|
28 |
27
|
eqeq1d |
|
29 |
|
oveq1 |
|
30 |
29
|
eqeq1d |
|
31 |
|
eqid |
|
32 |
1 3 31
|
mulgneg |
|
33 |
32
|
3expa |
|
34 |
4 31
|
grpinvid |
|
35 |
34
|
ad2antrr |
|
36 |
35
|
eqcomd |
|
37 |
33 36
|
eqeq12d |
|
38 |
|
simpll |
|
39 |
1 3
|
mulgcl |
|
40 |
39
|
3expa |
|
41 |
1 4
|
grpidcl |
|
42 |
41
|
ad2antrr |
|
43 |
1 31 38 40 42
|
grpinv11 |
|
44 |
37 43
|
bitrd |
|
45 |
30 44
|
sylan9bbr |
|
46 |
|
zre |
|
47 |
46
|
ad2antlr |
|
48 |
47
|
absord |
|
49 |
28 45 48
|
mpjaodan |
|
50 |
49
|
ralbidva |
|
51 |
50
|
adantr |
|
52 |
|
0dvds |
|
53 |
52
|
ad2antlr |
|
54 |
|
simprl |
|
55 |
54
|
breq1d |
|
56 |
|
zcn |
|
57 |
56
|
ad2antlr |
|
58 |
57
|
abs00ad |
|
59 |
53 55 58
|
3bitr4rd |
|
60 |
25 51 59
|
3imtr3d |
|
61 |
|
elrabi |
|
62 |
46
|
adantl |
|
63 |
|
nnrp |
|
64 |
|
modval |
|
65 |
62 63 64
|
syl2an |
|
66 |
65
|
adantr |
|
67 |
66
|
oveq1d |
|
68 |
|
simplll |
|
69 |
|
simpllr |
|
70 |
|
nnz |
|
71 |
70
|
ad2antlr |
|
72 |
|
rerpdivcl |
|
73 |
62 63 72
|
syl2an |
|
74 |
73
|
flcld |
|
75 |
74
|
adantr |
|
76 |
71 75
|
zmulcld |
|
77 |
|
simprl |
|
78 |
|
eqid |
|
79 |
1 3 78
|
mulgsubdir |
|
80 |
68 69 76 77 79
|
syl13anc |
|
81 |
|
simprr |
|
82 |
|
dvdsmul1 |
|
83 |
71 75 82
|
syl2anc |
|
84 |
1 2 3 4
|
gexdvdsi |
|
85 |
68 77 83 84
|
syl3anc |
|
86 |
81 85
|
oveq12d |
|
87 |
|
simpll |
|
88 |
1 4 78
|
grpsubid |
|
89 |
87 41 88
|
syl2anc2 |
|
90 |
89
|
adantr |
|
91 |
86 90
|
eqtrd |
|
92 |
67 80 91
|
3eqtrd |
|
93 |
92
|
expr |
|
94 |
93
|
ralimdva |
|
95 |
|
modlt |
|
96 |
62 63 95
|
syl2an |
|
97 |
|
zmodcl |
|
98 |
97
|
adantll |
|
99 |
98
|
nn0red |
|
100 |
|
nnre |
|
101 |
100
|
adantl |
|
102 |
99 101
|
ltnled |
|
103 |
96 102
|
mpbid |
|
104 |
1 2 3 4
|
gexlem2 |
|
105 |
|
elfzle2 |
|
106 |
104 105
|
syl |
|
107 |
106
|
3expia |
|
108 |
107
|
impancom |
|
109 |
108
|
con3d |
|
110 |
109
|
ex |
|
111 |
110
|
ad2antrr |
|
112 |
103 111
|
mpid |
|
113 |
|
elnn0 |
|
114 |
98 113
|
sylib |
|
115 |
114
|
ord |
|
116 |
94 112 115
|
3syld |
|
117 |
|
simpr |
|
118 |
|
simplr |
|
119 |
|
dvdsval3 |
|
120 |
117 118 119
|
syl2anc |
|
121 |
116 120
|
sylibrd |
|
122 |
61 121
|
sylan2 |
|
123 |
|
eqid |
|
124 |
1 3 4 2 123
|
gexlem1 |
|
125 |
124
|
adantr |
|
126 |
60 122 125
|
mpjaodan |
|
127 |
8 126
|
impbid |
|