Step |
Hyp |
Ref |
Expression |
1 |
|
df-4 |
|
2 |
1
|
oveq2i |
|
3 |
|
addcl |
|
4 |
|
3nn0 |
|
5 |
|
expp1 |
|
6 |
3 4 5
|
sylancl |
|
7 |
2 6
|
eqtrid |
|
8 |
|
binom3 |
|
9 |
8
|
oveq1d |
|
10 |
|
simpl |
|
11 |
|
expcl |
|
12 |
10 4 11
|
sylancl |
|
13 |
|
3cn |
|
14 |
10
|
sqcld |
|
15 |
|
simpr |
|
16 |
14 15
|
mulcld |
|
17 |
|
mulcl |
|
18 |
13 16 17
|
sylancr |
|
19 |
12 18
|
addcld |
|
20 |
15
|
sqcld |
|
21 |
10 20
|
mulcld |
|
22 |
|
mulcl |
|
23 |
13 21 22
|
sylancr |
|
24 |
|
expcl |
|
25 |
15 4 24
|
sylancl |
|
26 |
23 25
|
addcld |
|
27 |
19 26
|
addcld |
|
28 |
27 10 15
|
adddid |
|
29 |
1
|
oveq2i |
|
30 |
|
expp1 |
|
31 |
10 4 30
|
sylancl |
|
32 |
29 31
|
eqtr2id |
|
33 |
13
|
a1i |
|
34 |
33 16 10
|
mulassd |
|
35 |
14 15 10
|
mul32d |
|
36 |
|
df-3 |
|
37 |
36
|
oveq2i |
|
38 |
|
2nn0 |
|
39 |
|
expp1 |
|
40 |
10 38 39
|
sylancl |
|
41 |
37 40
|
eqtr2id |
|
42 |
41
|
oveq1d |
|
43 |
35 42
|
eqtrd |
|
44 |
43
|
oveq2d |
|
45 |
34 44
|
eqtrd |
|
46 |
32 45
|
oveq12d |
|
47 |
12 10 18 46
|
joinlmuladdmuld |
|
48 |
33 21 10
|
mulassd |
|
49 |
10 20 10
|
mul32d |
|
50 |
10
|
sqvald |
|
51 |
50
|
oveq1d |
|
52 |
49 51
|
eqtr4d |
|
53 |
52
|
oveq2d |
|
54 |
48 53
|
eqtrd |
|
55 |
25 10
|
mulcomd |
|
56 |
54 55
|
oveq12d |
|
57 |
23 10 25 56
|
joinlmuladdmuld |
|
58 |
47 57
|
oveq12d |
|
59 |
19 10 26 58
|
joinlmuladdmuld |
|
60 |
19 26 15
|
adddird |
|
61 |
33 16 15
|
mulassd |
|
62 |
14 15 15
|
mulassd |
|
63 |
15
|
sqvald |
|
64 |
63
|
oveq2d |
|
65 |
62 64
|
eqtr4d |
|
66 |
65
|
oveq2d |
|
67 |
61 66
|
eqtrd |
|
68 |
67
|
oveq2d |
|
69 |
12 15 18 68
|
joinlmuladdmuld |
|
70 |
33 21 15
|
mulassd |
|
71 |
10 20 15
|
mulassd |
|
72 |
36
|
oveq2i |
|
73 |
|
expp1 |
|
74 |
15 38 73
|
sylancl |
|
75 |
72 74
|
eqtr2id |
|
76 |
75
|
oveq2d |
|
77 |
71 76
|
eqtrd |
|
78 |
77
|
oveq2d |
|
79 |
70 78
|
eqtrd |
|
80 |
1
|
oveq2i |
|
81 |
|
expp1 |
|
82 |
15 4 81
|
sylancl |
|
83 |
80 82
|
eqtr2id |
|
84 |
79 83
|
oveq12d |
|
85 |
23 15 25 84
|
joinlmuladdmuld |
|
86 |
69 85
|
oveq12d |
|
87 |
12 15
|
mulcld |
|
88 |
14 20
|
mulcld |
|
89 |
|
mulcl |
|
90 |
13 88 89
|
sylancr |
|
91 |
10 25
|
mulcld |
|
92 |
|
mulcl |
|
93 |
13 91 92
|
sylancr |
|
94 |
|
4nn0 |
|
95 |
|
expcl |
|
96 |
15 94 95
|
sylancl |
|
97 |
93 96
|
addcld |
|
98 |
87 90 97
|
addassd |
|
99 |
60 86 98
|
3eqtrd |
|
100 |
59 99
|
oveq12d |
|
101 |
|
expcl |
|
102 |
10 94 101
|
sylancl |
|
103 |
|
mulcl |
|
104 |
13 87 103
|
sylancr |
|
105 |
102 104
|
addcld |
|
106 |
90 91
|
addcld |
|
107 |
90 97
|
addcld |
|
108 |
105 106 87 107
|
add4d |
|
109 |
102 104 87
|
addassd |
|
110 |
1
|
oveq1i |
|
111 |
|
ax-1cn |
|
112 |
111
|
a1i |
|
113 |
33 112 87
|
adddird |
|
114 |
110 113
|
eqtrid |
|
115 |
87
|
mulid2d |
|
116 |
115
|
oveq2d |
|
117 |
114 116
|
eqtrd |
|
118 |
117
|
oveq2d |
|
119 |
109 118
|
eqtr4d |
|
120 |
90 91 90 97
|
add4d |
|
121 |
|
3p3e6 |
|
122 |
121
|
oveq1i |
|
123 |
33 33 88
|
adddird |
|
124 |
122 123
|
eqtr3id |
|
125 |
|
3p1e4 |
|
126 |
13 111 125
|
addcomli |
|
127 |
126
|
oveq1i |
|
128 |
112 33 91
|
adddird |
|
129 |
127 128
|
eqtr3id |
|
130 |
91
|
mulid2d |
|
131 |
130
|
oveq1d |
|
132 |
129 131
|
eqtrd |
|
133 |
132
|
oveq1d |
|
134 |
91 93 96
|
addassd |
|
135 |
133 134
|
eqtrd |
|
136 |
124 135
|
oveq12d |
|
137 |
120 136
|
eqtr4d |
|
138 |
119 137
|
oveq12d |
|
139 |
108 138
|
eqtrd |
|
140 |
28 100 139
|
3eqtrd |
|
141 |
7 9 140
|
3eqtrd |
|