Step |
Hyp |
Ref |
Expression |
1 |
|
1nn0 |
|
2 |
|
5nn0 |
|
3 |
1 2
|
deccl |
|
4 |
3
|
nn0cni |
|
5 |
|
ax-icn |
|
6 |
|
8cn |
|
7 |
5 6
|
mulcli |
|
8 |
4 7
|
addcli |
|
9 |
|
imsqrtval |
|
10 |
8 9
|
ax-mp |
|
11 |
|
8pos |
|
12 |
|
0re |
|
13 |
|
8re |
|
14 |
12 13
|
ltnsymi |
|
15 |
3
|
nn0rei |
|
16 |
15 13
|
crimi |
|
17 |
16
|
breq1i |
|
18 |
14 17
|
sylnibr |
|
19 |
11 18
|
ax-mp |
|
20 |
19
|
iffalsei |
|
21 |
|
absreim |
|
22 |
15 13 21
|
mp2an |
|
23 |
4
|
sqvali |
|
24 |
|
eqid |
|
25 |
|
7nn0 |
|
26 |
4
|
mulid2i |
|
27 |
|
1p1e2 |
|
28 |
|
2nn0 |
|
29 |
25
|
nn0cni |
|
30 |
2
|
nn0cni |
|
31 |
|
7p5e12 |
|
32 |
29 30 31
|
addcomli |
|
33 |
1 2 25 26 27 28 32
|
decaddci |
|
34 |
30
|
mulid1i |
|
35 |
34
|
oveq1i |
|
36 |
|
5p2e7 |
|
37 |
35 36
|
eqtri |
|
38 |
|
5t5e25 |
|
39 |
2 1 2 24 2 28 37 38
|
decmul2c |
|
40 |
3 1 2 24 2 25 33 39
|
decmul1c |
|
41 |
23 40
|
eqtri |
|
42 |
6
|
sqvali |
|
43 |
|
8t8e64 |
|
44 |
42 43
|
eqtri |
|
45 |
41 44
|
oveq12i |
|
46 |
28 28
|
deccl |
|
47 |
|
6nn0 |
|
48 |
|
4nn0 |
|
49 |
|
eqid |
|
50 |
|
eqid |
|
51 |
|
eqid |
|
52 |
47
|
nn0cni |
|
53 |
28
|
nn0cni |
|
54 |
|
6p2e8 |
|
55 |
52 53 54
|
addcomli |
|
56 |
28 28 47 51 55
|
decaddi |
|
57 |
|
5p4e9 |
|
58 |
46 2 47 48 49 50 56 57
|
decadd |
|
59 |
1 25
|
deccl |
|
60 |
59
|
nn0cni |
|
61 |
60
|
sqvali |
|
62 |
|
eqid |
|
63 |
|
9nn0 |
|
64 |
1 1
|
deccl |
|
65 |
60
|
mulid2i |
|
66 |
|
eqid |
|
67 |
|
7p1e8 |
|
68 |
1 25 1 1 65 66 27 67
|
decadd |
|
69 |
29
|
mulid1i |
|
70 |
69
|
oveq1i |
|
71 |
|
7p4e11 |
|
72 |
70 71
|
eqtri |
|
73 |
|
7t7e49 |
|
74 |
25 1 25 62 63 48 72 73
|
decmul2c |
|
75 |
59 1 25 62 63 64 68 74
|
decmul1c |
|
76 |
61 75
|
eqtr2i |
|
77 |
45 58 76
|
3eqtri |
|
78 |
77
|
fveq2i |
|
79 |
59
|
nn0ge0i |
|
80 |
59
|
nn0rei |
|
81 |
80
|
sqrtsqi |
|
82 |
79 81
|
ax-mp |
|
83 |
22 78 82
|
3eqtri |
|
84 |
15 13
|
crrei |
|
85 |
83 84
|
oveq12i |
|
86 |
1 2 28 24 36
|
decaddi |
|
87 |
60 4 53 86
|
subaddrii |
|
88 |
85 87
|
eqtri |
|
89 |
88
|
oveq1i |
|
90 |
|
2div2e1 |
|
91 |
89 90
|
eqtri |
|
92 |
91
|
fveq2i |
|
93 |
|
sqrt1 |
|
94 |
92 93
|
eqtri |
|
95 |
20 94
|
oveq12i |
|
96 |
|
1t1e1 |
|
97 |
10 95 96
|
3eqtri |
|