Step |
Hyp |
Ref |
Expression |
1 |
|
df-3 |
|
2 |
1
|
oveq2i |
|
3 |
|
addcl |
|
4 |
|
2nn0 |
|
5 |
|
expp1 |
|
6 |
3 4 5
|
sylancl |
|
7 |
2 6
|
syl5eq |
|
8 |
|
sqcl |
|
9 |
3 8
|
syl |
|
10 |
|
simpl |
|
11 |
|
simpr |
|
12 |
9 10 11
|
adddid |
|
13 |
|
binom2 |
|
14 |
13
|
oveq1d |
|
15 |
|
sqcl |
|
16 |
10 15
|
syl |
|
17 |
|
2cn |
|
18 |
|
mulcl |
|
19 |
|
mulcl |
|
20 |
17 18 19
|
sylancr |
|
21 |
16 20
|
addcld |
|
22 |
|
sqcl |
|
23 |
11 22
|
syl |
|
24 |
21 23 10
|
adddird |
|
25 |
16 20 10
|
adddird |
|
26 |
1
|
oveq2i |
|
27 |
|
expp1 |
|
28 |
10 4 27
|
sylancl |
|
29 |
26 28
|
syl5eq |
|
30 |
|
sqval |
|
31 |
10 30
|
syl |
|
32 |
31
|
oveq1d |
|
33 |
10 10 11
|
mul32d |
|
34 |
32 33
|
eqtrd |
|
35 |
34
|
oveq2d |
|
36 |
|
2cnd |
|
37 |
36 18 10
|
mulassd |
|
38 |
35 37
|
eqtr4d |
|
39 |
29 38
|
oveq12d |
|
40 |
25 39
|
eqtr4d |
|
41 |
23 10
|
mulcomd |
|
42 |
40 41
|
oveq12d |
|
43 |
14 24 42
|
3eqtrd |
|
44 |
13
|
oveq1d |
|
45 |
21 23 11
|
adddird |
|
46 |
|
sqval |
|
47 |
11 46
|
syl |
|
48 |
47
|
oveq2d |
|
49 |
10 11 11
|
mulassd |
|
50 |
48 49
|
eqtr4d |
|
51 |
50
|
oveq2d |
|
52 |
36 18 11
|
mulassd |
|
53 |
51 52
|
eqtr4d |
|
54 |
53
|
oveq2d |
|
55 |
16 20 11
|
adddird |
|
56 |
54 55
|
eqtr4d |
|
57 |
1
|
oveq2i |
|
58 |
|
expp1 |
|
59 |
11 4 58
|
sylancl |
|
60 |
57 59
|
syl5eq |
|
61 |
56 60
|
oveq12d |
|
62 |
16 11
|
mulcld |
|
63 |
10 23
|
mulcld |
|
64 |
|
mulcl |
|
65 |
17 63 64
|
sylancr |
|
66 |
|
3nn0 |
|
67 |
|
expcl |
|
68 |
11 66 67
|
sylancl |
|
69 |
62 65 68
|
addassd |
|
70 |
61 69
|
eqtr3d |
|
71 |
44 45 70
|
3eqtrd |
|
72 |
43 71
|
oveq12d |
|
73 |
|
expcl |
|
74 |
10 66 73
|
sylancl |
|
75 |
|
mulcl |
|
76 |
17 62 75
|
sylancr |
|
77 |
74 76
|
addcld |
|
78 |
65 68
|
addcld |
|
79 |
77 63 62 78
|
add4d |
|
80 |
12 72 79
|
3eqtrd |
|
81 |
74 76 62
|
addassd |
|
82 |
1
|
oveq1i |
|
83 |
|
1cnd |
|
84 |
36 83 62
|
adddird |
|
85 |
82 84
|
syl5eq |
|
86 |
62
|
mulid2d |
|
87 |
86
|
oveq2d |
|
88 |
85 87
|
eqtrd |
|
89 |
88
|
oveq2d |
|
90 |
81 89
|
eqtr4d |
|
91 |
|
1p2e3 |
|
92 |
91
|
oveq1i |
|
93 |
83 36 63
|
adddird |
|
94 |
92 93
|
syl5eqr |
|
95 |
63
|
mulid2d |
|
96 |
95
|
oveq1d |
|
97 |
94 96
|
eqtrd |
|
98 |
97
|
oveq1d |
|
99 |
63 65 68
|
addassd |
|
100 |
98 99
|
eqtr2d |
|
101 |
90 100
|
oveq12d |
|
102 |
7 80 101
|
3eqtrd |
|