Step |
Hyp |
Ref |
Expression |
1 |
|
oveq2 |
|
2 |
|
oveq2 |
|
3 |
|
oveq2 |
|
4 |
2 3
|
oveq12d |
|
5 |
1 4
|
eqeq12d |
|
6 |
5
|
imbi2d |
|
7 |
|
oveq2 |
|
8 |
|
oveq2 |
|
9 |
|
oveq2 |
|
10 |
8 9
|
oveq12d |
|
11 |
7 10
|
eqeq12d |
|
12 |
11
|
imbi2d |
|
13 |
|
oveq2 |
|
14 |
|
oveq2 |
|
15 |
|
oveq2 |
|
16 |
14 15
|
oveq12d |
|
17 |
13 16
|
eqeq12d |
|
18 |
17
|
imbi2d |
|
19 |
|
oveq2 |
|
20 |
|
oveq2 |
|
21 |
|
oveq2 |
|
22 |
20 21
|
oveq12d |
|
23 |
19 22
|
eqeq12d |
|
24 |
23
|
imbi2d |
|
25 |
|
nnaddcl |
|
26 |
25
|
nnred |
|
27 |
|
ax-1rid |
|
28 |
26 27
|
syl |
|
29 |
|
nnre |
|
30 |
|
ax-1rid |
|
31 |
29 30
|
syl |
|
32 |
|
nnre |
|
33 |
|
ax-1rid |
|
34 |
32 33
|
syl |
|
35 |
31 34
|
oveqan12d |
|
36 |
28 35
|
eqtr4d |
|
37 |
|
simp2l |
|
38 |
|
simp2r |
|
39 |
37 38
|
nnaddcld |
|
40 |
39
|
nncnd |
|
41 |
|
simp1 |
|
42 |
41
|
nncnd |
|
43 |
|
1cnd |
|
44 |
40 42 43
|
adddid |
|
45 |
37
|
nnred |
|
46 |
45 30
|
syl |
|
47 |
46
|
oveq2d |
|
48 |
38
|
nnred |
|
49 |
48 33
|
syl |
|
50 |
49
|
oveq2d |
|
51 |
47 50
|
oveq12d |
|
52 |
37 41
|
nnmulcld |
|
53 |
52
|
nncnd |
|
54 |
37
|
nncnd |
|
55 |
38 41
|
nnmulcld |
|
56 |
55 38
|
nnaddcld |
|
57 |
56
|
nncnd |
|
58 |
53 54 57
|
addassd |
|
59 |
55
|
nncnd |
|
60 |
38
|
nncnd |
|
61 |
54 59 60
|
addassd |
|
62 |
61
|
oveq2d |
|
63 |
59 54 60
|
addassd |
|
64 |
63
|
oveq2d |
|
65 |
|
nnaddcom |
|
66 |
37 55 65
|
syl2anc |
|
67 |
66
|
oveq1d |
|
68 |
67
|
oveq2d |
|
69 |
53 59 40
|
addassd |
|
70 |
64 68 69
|
3eqtr4d |
|
71 |
58 62 70
|
3eqtr2d |
|
72 |
51 71
|
eqtrd |
|
73 |
54 42 43
|
adddid |
|
74 |
60 42 43
|
adddid |
|
75 |
73 74
|
oveq12d |
|
76 |
|
simp3 |
|
77 |
39
|
nnred |
|
78 |
77 27
|
syl |
|
79 |
76 78
|
oveq12d |
|
80 |
72 75 79
|
3eqtr4d |
|
81 |
44 80
|
eqtr4d |
|
82 |
81
|
3exp |
|
83 |
82
|
a2d |
|
84 |
6 12 18 24 36 83
|
nnind |
|
85 |
84
|
com12 |
|
86 |
85
|
3impia |
|