Step |
Hyp |
Ref |
Expression |
1 |
|
pgpfac1.k |
|
2 |
|
pgpfac1.s |
|
3 |
|
pgpfac1.b |
|
4 |
|
pgpfac1.o |
|
5 |
|
pgpfac1.e |
|
6 |
|
pgpfac1.z |
|
7 |
|
pgpfac1.l |
|
8 |
|
pgpfac1.p |
|
9 |
|
pgpfac1.g |
|
10 |
|
pgpfac1.n |
|
11 |
|
pgpfac1.oe |
|
12 |
|
pgpfac1.u |
|
13 |
|
pgpfac1.au |
|
14 |
|
pgpfac1.w |
|
15 |
|
pgpfac1.i |
|
16 |
|
pgpfac1.ss |
|
17 |
|
pgpfac1.2 |
|
18 |
|
pgpfac1.c |
|
19 |
|
pgpfac1.mg |
|
20 |
|
pgpfac1.m |
|
21 |
|
pgpfac1.mw |
|
22 |
18
|
eldifbd |
|
23 |
|
pgpprm |
|
24 |
8 23
|
syl |
|
25 |
|
ablgrp |
|
26 |
9 25
|
syl |
|
27 |
3 5
|
gexcl2 |
|
28 |
26 10 27
|
syl2anc |
|
29 |
|
pceq0 |
|
30 |
24 28 29
|
syl2anc |
|
31 |
|
oveq2 |
|
32 |
30 31
|
syl6bir |
|
33 |
3
|
grpbn0 |
|
34 |
26 33
|
syl |
|
35 |
|
hashnncl |
|
36 |
10 35
|
syl |
|
37 |
34 36
|
mpbird |
|
38 |
24 37
|
pccld |
|
39 |
3 5
|
gexdvds3 |
|
40 |
26 10 39
|
syl2anc |
|
41 |
3
|
pgphash |
|
42 |
8 10 41
|
syl2anc |
|
43 |
40 42
|
breqtrd |
|
44 |
|
oveq2 |
|
45 |
44
|
breq2d |
|
46 |
45
|
rspcev |
|
47 |
38 43 46
|
syl2anc |
|
48 |
|
pcprmpw2 |
|
49 |
24 28 48
|
syl2anc |
|
50 |
47 49
|
mpbid |
|
51 |
50
|
eqcomd |
|
52 |
|
prmnn |
|
53 |
24 52
|
syl |
|
54 |
53
|
nncnd |
|
55 |
54
|
exp0d |
|
56 |
51 55
|
eqeq12d |
|
57 |
|
grpmnd |
|
58 |
26 57
|
syl |
|
59 |
3 5
|
gex1 |
|
60 |
58 59
|
syl |
|
61 |
56 60
|
bitrd |
|
62 |
32 61
|
sylibd |
|
63 |
3
|
subgacs |
|
64 |
26 63
|
syl |
|
65 |
64
|
acsmred |
|
66 |
3
|
subgss |
|
67 |
12 66
|
syl |
|
68 |
67 13
|
sseldd |
|
69 |
1
|
mrcsncl |
|
70 |
65 68 69
|
syl2anc |
|
71 |
2 70
|
eqeltrid |
|
72 |
7
|
lsmsubg2 |
|
73 |
9 71 14 72
|
syl3anc |
|
74 |
6
|
subg0cl |
|
75 |
73 74
|
syl |
|
76 |
75
|
snssd |
|
77 |
76
|
adantr |
|
78 |
18
|
eldifad |
|
79 |
67 78
|
sseldd |
|
80 |
79
|
adantr |
|
81 |
3 6
|
grpidcl |
|
82 |
26 81
|
syl |
|
83 |
|
en1eqsn |
|
84 |
82 83
|
sylan |
|
85 |
80 84
|
eleqtrd |
|
86 |
77 85
|
sseldd |
|
87 |
86
|
ex |
|
88 |
62 87
|
syld |
|
89 |
22 88
|
mt3d |
|
90 |
28
|
nncnd |
|
91 |
53
|
nnne0d |
|
92 |
90 54 91
|
divcan1d |
|
93 |
11 92
|
eqtr4d |
|
94 |
|
nndivdvds |
|
95 |
28 53 94
|
syl2anc |
|
96 |
89 95
|
mpbid |
|
97 |
96
|
nnzd |
|
98 |
97 20
|
zmulcld |
|
99 |
68
|
snssd |
|
100 |
65 1 99
|
mrcssidd |
|
101 |
100 2
|
sseqtrrdi |
|
102 |
|
snssg |
|
103 |
13 102
|
syl |
|
104 |
101 103
|
mpbird |
|
105 |
19
|
subgmulgcl |
|
106 |
71 98 104 105
|
syl3anc |
|
107 |
|
prmz |
|
108 |
24 107
|
syl |
|
109 |
3 19
|
mulgcl |
|
110 |
26 108 79 109
|
syl3anc |
|
111 |
3 19
|
mulgcl |
|
112 |
26 20 68 111
|
syl3anc |
|
113 |
|
eqid |
|
114 |
3 19 113
|
mulgdi |
|
115 |
9 97 110 112 114
|
syl13anc |
|
116 |
92
|
oveq1d |
|
117 |
3 19
|
mulgass |
|
118 |
26 97 108 79 117
|
syl13anc |
|
119 |
3 5 19 6
|
gexid |
|
120 |
79 119
|
syl |
|
121 |
116 118 120
|
3eqtr3rd |
|
122 |
3 19
|
mulgass |
|
123 |
26 97 20 68 122
|
syl13anc |
|
124 |
121 123
|
oveq12d |
|
125 |
3
|
subgss |
|
126 |
71 125
|
syl |
|
127 |
126 106
|
sseldd |
|
128 |
3 113 6
|
grplid |
|
129 |
26 127 128
|
syl2anc |
|
130 |
115 124 129
|
3eqtr2d |
|
131 |
19
|
subgmulgcl |
|
132 |
14 97 21 131
|
syl3anc |
|
133 |
130 132
|
eqeltrrd |
|
134 |
106 133
|
elind |
|
135 |
134 15
|
eleqtrd |
|
136 |
|
elsni |
|
137 |
135 136
|
syl |
|
138 |
3 4 19 6
|
oddvds |
|
139 |
26 68 98 138
|
syl3anc |
|
140 |
137 139
|
mpbird |
|
141 |
93 140
|
eqbrtrrd |
|
142 |
96
|
nnne0d |
|
143 |
|
dvdscmulr |
|
144 |
108 20 97 142 143
|
syl112anc |
|
145 |
141 144
|
mpbid |
|
146 |
89 145
|
jca |
|