Step |
Hyp |
Ref |
Expression |
1 |
|
siii.1 |
|
2 |
|
siii.6 |
|
3 |
|
siii.7 |
|
4 |
|
siii.9 |
|
5 |
|
siii.a |
|
6 |
|
siii.b |
|
7 |
|
sii1.3 |
|
8 |
|
sii1.4 |
|
9 |
|
sii1.c |
|
10 |
|
sii1.r |
|
11 |
|
sii1.z |
|
12 |
4
|
phnvi |
|
13 |
9
|
cjcli |
|
14 |
1 8
|
nvscl |
|
15 |
12 13 6 14
|
mp3an |
|
16 |
1 7
|
nvmcl |
|
17 |
12 5 15 16
|
mp3an |
|
18 |
1 2 12 17
|
nvcli |
|
19 |
18
|
sqge0i |
|
20 |
17 5 15
|
3pm3.2i |
|
21 |
1 7 3
|
dipsubdi |
|
22 |
4 20 21
|
mp2an |
|
23 |
1 2 3
|
ipidsq |
|
24 |
12 17 23
|
mp2an |
|
25 |
13 6 15
|
3pm3.2i |
|
26 |
1 8 3
|
dipass |
|
27 |
4 25 26
|
mp2an |
|
28 |
6 9 6
|
3pm3.2i |
|
29 |
1 8 3
|
dipassr2 |
|
30 |
4 28 29
|
mp2an |
|
31 |
1 2 3
|
ipidsq |
|
32 |
12 6 31
|
mp2an |
|
33 |
32
|
oveq2i |
|
34 |
30 33
|
eqtri |
|
35 |
34
|
oveq2i |
|
36 |
27 35
|
eqtri |
|
37 |
36
|
oveq2i |
|
38 |
37
|
oveq2i |
|
39 |
1 2 12 5
|
nvcli |
|
40 |
39
|
recni |
|
41 |
40
|
sqcli |
|
42 |
1 3
|
dipcl |
|
43 |
12 6 5 42
|
mp3an |
|
44 |
13 43
|
mulcli |
|
45 |
10
|
recni |
|
46 |
1 2 12 6
|
nvcli |
|
47 |
46
|
recni |
|
48 |
47
|
sqcli |
|
49 |
9 48
|
mulcli |
|
50 |
13 49
|
mulcli |
|
51 |
|
sub4 |
|
52 |
41 44 45 50 51
|
mp4an |
|
53 |
38 52
|
eqtri |
|
54 |
5 15 5
|
3pm3.2i |
|
55 |
1 7 3
|
dipsubdir |
|
56 |
4 54 55
|
mp2an |
|
57 |
1 2 3
|
ipidsq |
|
58 |
12 5 57
|
mp2an |
|
59 |
13 6 5
|
3pm3.2i |
|
60 |
1 8 3
|
dipass |
|
61 |
4 59 60
|
mp2an |
|
62 |
58 61
|
oveq12i |
|
63 |
56 62
|
eqtri |
|
64 |
5 15 15
|
3pm3.2i |
|
65 |
1 7 3
|
dipsubdir |
|
66 |
4 64 65
|
mp2an |
|
67 |
5 9 6
|
3pm3.2i |
|
68 |
1 8 3
|
dipassr2 |
|
69 |
4 67 68
|
mp2an |
|
70 |
69
|
oveq1i |
|
71 |
66 70
|
eqtri |
|
72 |
63 71
|
oveq12i |
|
73 |
13 43 49
|
subdii |
|
74 |
73
|
oveq2i |
|
75 |
53 72 74
|
3eqtr4i |
|
76 |
22 24 75
|
3eqtr3i |
|
77 |
19 76
|
breqtri |
|
78 |
43 49
|
subeq0i |
|
79 |
|
oveq2 |
|
80 |
13
|
mul01i |
|
81 |
79 80
|
eqtrdi |
|
82 |
78 81
|
sylbir |
|
83 |
82
|
oveq2d |
|
84 |
39
|
resqcli |
|
85 |
84
|
recni |
|
86 |
85 45
|
subcli |
|
87 |
86
|
subid1i |
|
88 |
83 87
|
eqtrdi |
|
89 |
77 88
|
breqtrid |
|
90 |
84 10
|
subge0i |
|
91 |
89 90
|
sylib |
|
92 |
46
|
resqcli |
|
93 |
46
|
sqge0i |
|
94 |
92 93
|
pm3.2i |
|
95 |
10 84 94
|
3pm3.2i |
|
96 |
|
lemul1a |
|
97 |
95 96
|
mpan |
|
98 |
91 97
|
syl |
|
99 |
40 47
|
sqmuli |
|
100 |
98 99
|
breqtrrdi |
|
101 |
10 92
|
mulge0i |
|
102 |
11 93 101
|
mp2an |
|
103 |
39 46
|
remulcli |
|
104 |
103
|
sqge0i |
|
105 |
10 92
|
remulcli |
|
106 |
103
|
resqcli |
|
107 |
105 106
|
sqrtlei |
|
108 |
102 104 107
|
mp2an |
|
109 |
100 108
|
sylib |
|
110 |
1 3
|
dipcl |
|
111 |
12 5 6 110
|
mp3an |
|
112 |
9 111
|
mulcomi |
|
113 |
112
|
oveq1i |
|
114 |
92
|
recni |
|
115 |
111 9 114
|
mulassi |
|
116 |
113 115
|
eqtri |
|
117 |
116
|
fveq2i |
|
118 |
1 2
|
nvge0 |
|
119 |
12 5 118
|
mp2an |
|
120 |
1 2
|
nvge0 |
|
121 |
12 6 120
|
mp2an |
|
122 |
39 46
|
mulge0i |
|
123 |
119 121 122
|
mp2an |
|
124 |
103
|
sqrtsqi |
|
125 |
123 124
|
ax-mp |
|
126 |
109 117 125
|
3brtr3g |
|