Step |
Hyp |
Ref |
Expression |
1 |
|
pjthlem.v |
|
2 |
|
pjthlem.n |
|
3 |
|
pjthlem.p |
|
4 |
|
pjthlem.m |
|
5 |
|
pjthlem.h |
|
6 |
|
pjthlem.l |
|
7 |
|
pjthlem.1 |
|
8 |
|
pjthlem.2 |
|
9 |
|
pjthlem.4 |
|
10 |
|
pjthlem.5 |
|
11 |
|
pjthlem.7 |
|
12 |
|
pjthlem.8 |
|
13 |
|
hlcph |
|
14 |
7 13
|
syl |
|
15 |
1 6
|
lssss |
|
16 |
8 15
|
syl |
|
17 |
16 10
|
sseldd |
|
18 |
1 5
|
cphipcl |
|
19 |
14 9 17 18
|
syl3anc |
|
20 |
19
|
abscld |
|
21 |
20
|
recnd |
|
22 |
20
|
resqcld |
|
23 |
22
|
renegcld |
|
24 |
1 5
|
reipcl |
|
25 |
14 17 24
|
syl2anc |
|
26 |
|
2re |
|
27 |
|
readdcl |
|
28 |
25 26 27
|
sylancl |
|
29 |
|
0red |
|
30 |
|
peano2re |
|
31 |
25 30
|
syl |
|
32 |
1 5
|
ipge0 |
|
33 |
14 17 32
|
syl2anc |
|
34 |
25
|
ltp1d |
|
35 |
29 25 31 33 34
|
lelttrd |
|
36 |
31
|
ltp1d |
|
37 |
|
df-2 |
|
38 |
37
|
oveq2i |
|
39 |
25
|
recnd |
|
40 |
|
ax-1cn |
|
41 |
|
addass |
|
42 |
40 40 41
|
mp3an23 |
|
43 |
39 42
|
syl |
|
44 |
38 43
|
eqtr4id |
|
45 |
36 44
|
breqtrrd |
|
46 |
29 31 28 35 45
|
lttrd |
|
47 |
28 46
|
elrpd |
|
48 |
|
oveq2 |
|
49 |
48
|
fveq2d |
|
50 |
49
|
breq2d |
|
51 |
|
cphlmod |
|
52 |
14 51
|
syl |
|
53 |
|
hlphl |
|
54 |
7 53
|
syl |
|
55 |
|
eqid |
|
56 |
|
eqid |
|
57 |
55 5 1 56
|
ipcl |
|
58 |
54 9 17 57
|
syl3anc |
|
59 |
55 56
|
hlress |
|
60 |
7 59
|
syl |
|
61 |
60 31
|
sseldd |
|
62 |
25 33
|
ge0p1rpd |
|
63 |
62
|
rpne0d |
|
64 |
55 56
|
cphdivcl |
|
65 |
14 58 61 63 64
|
syl13anc |
|
66 |
12 65
|
eqeltrid |
|
67 |
|
eqid |
|
68 |
55 67 56 6
|
lssvscl |
|
69 |
52 8 66 10 68
|
syl22anc |
|
70 |
50 11 69
|
rspcdva |
|
71 |
|
cphngp |
|
72 |
14 71
|
syl |
|
73 |
1 2
|
nmcl |
|
74 |
72 9 73
|
syl2anc |
|
75 |
1 55 67 56
|
lmodvscl |
|
76 |
52 66 17 75
|
syl3anc |
|
77 |
1 4
|
lmodvsubcl |
|
78 |
52 9 76 77
|
syl3anc |
|
79 |
1 2
|
nmcl |
|
80 |
72 78 79
|
syl2anc |
|
81 |
1 2
|
nmge0 |
|
82 |
72 9 81
|
syl2anc |
|
83 |
1 2
|
nmge0 |
|
84 |
72 78 83
|
syl2anc |
|
85 |
74 80 82 84
|
le2sqd |
|
86 |
70 85
|
mpbid |
|
87 |
80
|
resqcld |
|
88 |
74
|
resqcld |
|
89 |
87 88
|
subge0d |
|
90 |
86 89
|
mpbird |
|
91 |
|
2z |
|
92 |
|
rpexpcl |
|
93 |
62 91 92
|
sylancl |
|
94 |
22 93
|
rerpdivcld |
|
95 |
94 28
|
remulcld |
|
96 |
95
|
recnd |
|
97 |
96
|
negcld |
|
98 |
1 5
|
cphipcl |
|
99 |
14 9 9 98
|
syl3anc |
|
100 |
97 99
|
pncand |
|
101 |
1 5 2
|
nmsq |
|
102 |
14 78 101
|
syl2anc |
|
103 |
5 1 4
|
cphsubdir |
|
104 |
14 9 76 78 103
|
syl13anc |
|
105 |
5 1 4
|
cphsubdi |
|
106 |
14 9 9 76 105
|
syl13anc |
|
107 |
106
|
oveq1d |
|
108 |
1 5
|
cphipcl |
|
109 |
14 9 76 108
|
syl3anc |
|
110 |
5 1 4
|
cphsubdi |
|
111 |
14 76 9 76 110
|
syl13anc |
|
112 |
1 5
|
cphipcl |
|
113 |
14 76 9 112
|
syl3anc |
|
114 |
1 5
|
cphipcl |
|
115 |
14 76 76 114
|
syl3anc |
|
116 |
113 115
|
subcld |
|
117 |
111 116
|
eqeltrd |
|
118 |
99 109 117
|
subsub4d |
|
119 |
94
|
recnd |
|
120 |
31
|
recnd |
|
121 |
|
1cnd |
|
122 |
119 120 121
|
adddid |
|
123 |
44
|
oveq2d |
|
124 |
5 1 55 56 67
|
cphassr |
|
125 |
14 66 9 17 124
|
syl13anc |
|
126 |
19 120 63
|
divcld |
|
127 |
12 126
|
eqeltrid |
|
128 |
127
|
cjcld |
|
129 |
128 19
|
mulcomd |
|
130 |
19
|
cjcld |
|
131 |
19 130 120 63
|
divassd |
|
132 |
19
|
absvalsqd |
|
133 |
132
|
oveq1d |
|
134 |
12
|
fveq2i |
|
135 |
19 120 63
|
cjdivd |
|
136 |
31
|
cjred |
|
137 |
136
|
oveq2d |
|
138 |
135 137
|
eqtrd |
|
139 |
134 138
|
syl5eq |
|
140 |
139
|
oveq2d |
|
141 |
131 133 140
|
3eqtr4rd |
|
142 |
125 129 141
|
3eqtrd |
|
143 |
22
|
recnd |
|
144 |
143 120
|
mulcomd |
|
145 |
120
|
sqvald |
|
146 |
144 145
|
oveq12d |
|
147 |
143 120 120 63 63
|
divcan5d |
|
148 |
146 147
|
eqtr2d |
|
149 |
93
|
rpcnd |
|
150 |
93
|
rpne0d |
|
151 |
143 120 149 150
|
div23d |
|
152 |
142 148 151
|
3eqtrd |
|
153 |
94 31
|
remulcld |
|
154 |
152 153
|
eqeltrd |
|
155 |
154
|
cjred |
|
156 |
5 1
|
cphipcj |
|
157 |
14 9 76 156
|
syl3anc |
|
158 |
155 157 152
|
3eqtr3d |
|
159 |
5 1 55 56 67
|
cph2ass |
|
160 |
14 66 66 17 17 159
|
syl122anc |
|
161 |
12
|
fveq2i |
|
162 |
19 120 63
|
absdivd |
|
163 |
62
|
rpge0d |
|
164 |
31 163
|
absidd |
|
165 |
164
|
oveq2d |
|
166 |
162 165
|
eqtrd |
|
167 |
161 166
|
syl5eq |
|
168 |
167
|
oveq1d |
|
169 |
127
|
absvalsqd |
|
170 |
21 120 63
|
sqdivd |
|
171 |
168 169 170
|
3eqtr3d |
|
172 |
171
|
oveq1d |
|
173 |
160 172
|
eqtrd |
|
174 |
158 173
|
oveq12d |
|
175 |
|
pncan2 |
|
176 |
39 40 175
|
sylancl |
|
177 |
176
|
oveq2d |
|
178 |
119 120 39
|
subdid |
|
179 |
177 178
|
eqtr3d |
|
180 |
174 111 179
|
3eqtr4d |
|
181 |
152 180
|
oveq12d |
|
182 |
122 123 181
|
3eqtr4rd |
|
183 |
182
|
oveq2d |
|
184 |
107 118 183
|
3eqtrd |
|
185 |
102 104 184
|
3eqtrd |
|
186 |
99 96
|
negsubd |
|
187 |
99 97
|
addcomd |
|
188 |
185 186 187
|
3eqtr2d |
|
189 |
1 5 2
|
nmsq |
|
190 |
14 9 189
|
syl2anc |
|
191 |
188 190
|
oveq12d |
|
192 |
28
|
renegcld |
|
193 |
192
|
recnd |
|
194 |
143 193 149 150
|
div23d |
|
195 |
28
|
recnd |
|
196 |
119 195
|
mulneg2d |
|
197 |
194 196
|
eqtrd |
|
198 |
100 191 197
|
3eqtr4rd |
|
199 |
90 198
|
breqtrrd |
|
200 |
22 192
|
remulcld |
|
201 |
200 93
|
ge0divd |
|
202 |
199 201
|
mpbird |
|
203 |
|
mulneg12 |
|
204 |
143 195 203
|
syl2anc |
|
205 |
202 204
|
breqtrrd |
|
206 |
23 47 205
|
prodge0ld |
|
207 |
22
|
le0neg1d |
|
208 |
206 207
|
mpbird |
|
209 |
20
|
sqge0d |
|
210 |
|
0re |
|
211 |
|
letri3 |
|
212 |
22 210 211
|
sylancl |
|
213 |
208 209 212
|
mpbir2and |
|
214 |
21 213
|
sqeq0d |
|
215 |
19 214
|
abs00d |
|