Step |
Hyp |
Ref |
Expression |
1 |
|
cphipfval.x |
|
2 |
|
cphipfval.p |
|
3 |
|
cphipfval.s |
|
4 |
|
cphipfval.n |
|
5 |
|
cphipfval.i |
|
6 |
|
cphipval2.m |
|
7 |
|
cphipval2.f |
|
8 |
|
cphipval2.k |
|
9 |
|
simpl |
|
10 |
9
|
3ad2ant1 |
|
11 |
|
cphngp |
|
12 |
11
|
adantr |
|
13 |
|
ngpgrp |
|
14 |
12 13
|
syl |
|
15 |
1 2
|
grpcl |
|
16 |
14 15
|
syl3an1 |
|
17 |
1 5 4
|
nmsq |
|
18 |
10 16 17
|
syl2anc |
|
19 |
|
simp2 |
|
20 |
|
simp3 |
|
21 |
5 1 2 10 19 20 19 20
|
cph2di |
|
22 |
18 21
|
eqtrd |
|
23 |
1 6
|
grpsubcl |
|
24 |
14 23
|
syl3an1 |
|
25 |
1 5 4
|
nmsq |
|
26 |
10 24 25
|
syl2anc |
|
27 |
5 1 6 10 19 20 19 20
|
cph2subdi |
|
28 |
26 27
|
eqtrd |
|
29 |
22 28
|
oveq12d |
|
30 |
1 5
|
reipcl |
|
31 |
30
|
adantlr |
|
32 |
31
|
recnd |
|
33 |
32
|
3adant3 |
|
34 |
1 5
|
reipcl |
|
35 |
34
|
adantlr |
|
36 |
35
|
recnd |
|
37 |
36
|
3adant2 |
|
38 |
33 37
|
addcld |
|
39 |
1 5
|
cphipcl |
|
40 |
9 39
|
syl3an1 |
|
41 |
1 5
|
cphipcl |
|
42 |
9 41
|
syl3an1 |
|
43 |
42
|
3com23 |
|
44 |
40 43
|
addcld |
|
45 |
38 44 44
|
pnncand |
|
46 |
29 45
|
eqtrd |
|
47 |
14
|
3ad2ant1 |
|
48 |
|
cphlmod |
|
49 |
48
|
adantr |
|
50 |
49
|
adantr |
|
51 |
|
simplr |
|
52 |
|
simpr |
|
53 |
1 7 3 8
|
lmodvscl |
|
54 |
50 51 52 53
|
syl3anc |
|
55 |
54
|
3adant2 |
|
56 |
1 2
|
grpcl |
|
57 |
47 19 55 56
|
syl3anc |
|
58 |
1 5 4
|
nmsq |
|
59 |
10 57 58
|
syl2anc |
|
60 |
5 1 2 10 19 55 19 55
|
cph2di |
|
61 |
59 60
|
eqtrd |
|
62 |
1 6
|
grpsubcl |
|
63 |
47 19 55 62
|
syl3anc |
|
64 |
1 5 4
|
nmsq |
|
65 |
10 63 64
|
syl2anc |
|
66 |
5 1 6 10 19 55 19 55
|
cph2subdi |
|
67 |
65 66
|
eqtrd |
|
68 |
61 67
|
oveq12d |
|
69 |
68
|
oveq2d |
|
70 |
1 5
|
cphipcl |
|
71 |
10 55 55 70
|
syl3anc |
|
72 |
33 71
|
addcld |
|
73 |
1 5
|
cphipcl |
|
74 |
10 19 55 73
|
syl3anc |
|
75 |
1 5
|
cphipcl |
|
76 |
10 55 19 75
|
syl3anc |
|
77 |
74 76
|
addcld |
|
78 |
72 77 77
|
pnncand |
|
79 |
78
|
oveq2d |
|
80 |
1 3 5 7 8
|
cphassir |
|
81 |
1 3 5 7 8
|
cphassi |
|
82 |
80 81
|
oveq12d |
|
83 |
82 82
|
oveq12d |
|
84 |
83
|
oveq2d |
|
85 |
|
ax-icn |
|
86 |
85
|
a1i |
|
87 |
|
negicn |
|
88 |
87
|
a1i |
|
89 |
88 40
|
mulcld |
|
90 |
86 43
|
mulcld |
|
91 |
89 90
|
addcld |
|
92 |
86 91 91
|
adddid |
|
93 |
86 89 90
|
adddid |
|
94 |
86 88 40
|
mulassd |
|
95 |
85 85
|
mulneg2i |
|
96 |
|
ixi |
|
97 |
96
|
negeqi |
|
98 |
|
negneg1e1 |
|
99 |
95 97 98
|
3eqtri |
|
100 |
99
|
oveq1i |
|
101 |
94 100
|
eqtr3di |
|
102 |
86 86 43
|
mulassd |
|
103 |
96
|
oveq1i |
|
104 |
102 103
|
eqtr3di |
|
105 |
101 104
|
oveq12d |
|
106 |
93 105
|
eqtrd |
|
107 |
106 106
|
oveq12d |
|
108 |
40
|
mulid2d |
|
109 |
108
|
oveq1d |
|
110 |
|
addneg1mul |
|
111 |
40 43 110
|
syl2anc |
|
112 |
109 111
|
eqtrd |
|
113 |
112 112
|
oveq12d |
|
114 |
107 113
|
eqtrd |
|
115 |
84 92 114
|
3eqtrd |
|
116 |
69 79 115
|
3eqtrd |
|
117 |
46 116
|
oveq12d |
|
118 |
117
|
oveq1d |
|
119 |
40 43
|
subcld |
|
120 |
44 44 119 119
|
add4d |
|
121 |
40 43 40
|
ppncand |
|
122 |
121 121
|
oveq12d |
|
123 |
120 122
|
eqtrd |
|
124 |
123
|
oveq1d |
|
125 |
40
|
2timesd |
|
126 |
125
|
eqcomd |
|
127 |
126 126
|
oveq12d |
|
128 |
|
2cnd |
|
129 |
128 128 40
|
adddird |
|
130 |
|
2p2e4 |
|
131 |
130
|
a1i |
|
132 |
131
|
oveq1d |
|
133 |
127 129 132
|
3eqtr2d |
|
134 |
133
|
oveq1d |
|
135 |
|
4cn |
|
136 |
135
|
a1i |
|
137 |
|
4ne0 |
|
138 |
137
|
a1i |
|
139 |
40 136 138
|
divcan3d |
|
140 |
134 139
|
eqtrd |
|
141 |
118 124 140
|
3eqtrrd |
|