Step |
Hyp |
Ref |
Expression |
1 |
|
flt4lem5a.m |
|
2 |
|
flt4lem5a.n |
|
3 |
|
flt4lem5a.r |
|
4 |
|
flt4lem5a.s |
|
5 |
|
flt4lem5a.a |
|
6 |
|
flt4lem5a.b |
|
7 |
|
flt4lem5a.c |
|
8 |
|
flt4lem5a.1 |
|
9 |
|
flt4lem5a.2 |
|
10 |
|
flt4lem5a.3 |
|
11 |
5
|
nnsqcld |
|
12 |
6
|
nnsqcld |
|
13 |
|
2prm |
|
14 |
5
|
nnzd |
|
15 |
|
prmdvdssq |
|
16 |
13 14 15
|
sylancr |
|
17 |
8 16
|
mtbid |
|
18 |
|
2nn |
|
19 |
18
|
a1i |
|
20 |
|
rplpwr |
|
21 |
5 7 19 20
|
syl3anc |
|
22 |
9 21
|
mpd |
|
23 |
5
|
nncnd |
|
24 |
23
|
flt4lem |
|
25 |
6
|
nncnd |
|
26 |
25
|
flt4lem |
|
27 |
24 26
|
oveq12d |
|
28 |
27 10
|
eqtr3d |
|
29 |
11 12 7 17 22 28
|
flt4lem1 |
|
30 |
2
|
pythagtriplem13 |
|
31 |
29 30
|
syl |
|
32 |
1
|
pythagtriplem11 |
|
33 |
29 32
|
syl |
|
34 |
1 2 3 4 5 6 7 8 9 10
|
flt4lem5a |
|
35 |
31
|
nnzd |
|
36 |
14 35
|
gcdcomd |
|
37 |
33
|
nnzd |
|
38 |
35 37
|
gcdcomd |
|
39 |
1 2
|
flt4lem5 |
|
40 |
29 39
|
syl |
|
41 |
38 40
|
eqtrd |
|
42 |
31
|
nnsqcld |
|
43 |
42
|
nncnd |
|
44 |
11
|
nncnd |
|
45 |
43 44
|
addcomd |
|
46 |
45 34
|
eqtrd |
|
47 |
31 5 33 41 46
|
fltabcoprm |
|
48 |
36 47
|
eqtrd |
|
49 |
3 4
|
flt4lem5 |
|
50 |
5 31 33 34 48 8 49
|
syl312anc |
|
51 |
3
|
pythagtriplem11 |
|
52 |
5 31 33 34 48 8 51
|
syl312anc |
|
53 |
4
|
pythagtriplem13 |
|
54 |
5 31 33 34 48 8 53
|
syl312anc |
|
55 |
1 2 3 4 5 6 7 8 9 10
|
flt4lem5d |
|
56 |
33 52 54 55 50
|
flt4lem5elem |
|
57 |
50 56
|
jca |
|
58 |
|
3anass |
|
59 |
57 58
|
sylibr |
|
60 |
52 54 33
|
3jca |
|
61 |
|
sq2 |
|
62 |
|
4cn |
|
63 |
61 62
|
eqeltri |
|
64 |
63
|
a1i |
|
65 |
52 54
|
nnmulcld |
|
66 |
33 65
|
nnmulcld |
|
67 |
66
|
nncnd |
|
68 |
|
4ne0 |
|
69 |
61 68
|
eqnetri |
|
70 |
69
|
a1i |
|
71 |
|
2cn |
|
72 |
71
|
sqvali |
|
73 |
72
|
oveq1i |
|
74 |
|
2cnd |
|
75 |
33
|
nncnd |
|
76 |
65
|
nncnd |
|
77 |
74 74 75 76
|
mul4d |
|
78 |
1 2 3 4 5 6 7 8 9 10
|
flt4lem5c |
|
79 |
78
|
eqcomd |
|
80 |
79 31
|
eqeltrd |
|
81 |
80
|
nncnd |
|
82 |
74 75 81
|
mulassd |
|
83 |
79
|
oveq2d |
|
84 |
83
|
oveq2d |
|
85 |
82 84
|
eqtrd |
|
86 |
1 2 3 4 5 6 7 8 9 10
|
flt4lem5b |
|
87 |
77 85 86
|
3eqtrd |
|
88 |
73 87
|
syl5eq |
|
89 |
64 67 70 88
|
mvllmuld |
|
90 |
|
2ne0 |
|
91 |
90
|
a1i |
|
92 |
25 74 91
|
sqdivd |
|
93 |
89 92
|
eqtr4d |
|
94 |
66
|
nnzd |
|
95 |
93 94
|
eqeltrrd |
|
96 |
6
|
nnzd |
|
97 |
|
znq |
|
98 |
96 18 97
|
sylancl |
|
99 |
6
|
nngt0d |
|
100 |
6
|
nnred |
|
101 |
|
halfpos2 |
|
102 |
100 101
|
syl |
|
103 |
99 102
|
mpbid |
|
104 |
95 98 103
|
posqsqznn |
|
105 |
93 104
|
jca |
|
106 |
59 60 105
|
3jca |
|