Step |
Hyp |
Ref |
Expression |
1 |
|
tru |
|
2 |
|
8lt9 |
|
3 |
|
2z |
|
4 |
|
uzid |
|
5 |
3 4
|
ax-mp |
|
6 |
|
8nn |
|
7 |
|
nnrp |
|
8 |
6 7
|
ax-mp |
|
9 |
|
9nn |
|
10 |
|
nnrp |
|
11 |
9 10
|
ax-mp |
|
12 |
5 8 11
|
3pm3.2i |
|
13 |
|
logblt |
|
14 |
12 13
|
ax-mp |
|
15 |
2 14
|
mpbi |
|
16 |
15
|
a1i |
|
17 |
|
eqid |
|
18 |
|
cu2 |
|
19 |
17 18
|
eqtr4i |
|
20 |
19
|
a1i |
|
21 |
20
|
oveq2d |
|
22 |
|
2rp |
|
23 |
22
|
a1i |
|
24 |
|
1red |
|
25 |
|
1lt2 |
|
26 |
25
|
a1i |
|
27 |
24 26
|
ltned |
|
28 |
27
|
necomd |
|
29 |
|
3z |
|
30 |
29
|
a1i |
|
31 |
23 28 30
|
relogbexpd |
|
32 |
21 31
|
eqtrd |
|
33 |
|
eqid |
|
34 |
|
sq3 |
|
35 |
33 34
|
eqtr4i |
|
36 |
35
|
a1i |
|
37 |
36
|
oveq2d |
|
38 |
16 32 37
|
3brtr3d |
|
39 |
|
3re |
|
40 |
39
|
a1i |
|
41 |
40
|
recnd |
|
42 |
|
2re |
|
43 |
42
|
a1i |
|
44 |
43
|
recnd |
|
45 |
|
2pos |
|
46 |
45
|
a1i |
|
47 |
46
|
gt0ne0d |
|
48 |
41 44 47
|
divcan1d |
|
49 |
48
|
eqcomd |
|
50 |
|
3pos |
|
51 |
50
|
a1i |
|
52 |
40 51
|
elrpd |
|
53 |
3
|
a1i |
|
54 |
23 28 52 53
|
relogbzexpd |
|
55 |
43 46 40 51 28
|
relogbcld |
|
56 |
55
|
recnd |
|
57 |
44 56
|
mulcomd |
|
58 |
54 57
|
eqtrd |
|
59 |
38 49 58
|
3brtr3d |
|
60 |
40
|
rehalfcld |
|
61 |
60 55 23
|
ltmul1d |
|
62 |
59 61
|
mpbird |
|
63 |
|
2nn0 |
|
64 |
|
3nn0 |
|
65 |
|
7nn0 |
|
66 |
|
7lt10 |
|
67 |
|
2lt3 |
|
68 |
63 64 65 63 66 67
|
decltc |
|
69 |
|
7nn |
|
70 |
63 69
|
decnncl |
|
71 |
|
nnrp |
|
72 |
70 71
|
ax-mp |
|
73 |
|
2nn |
|
74 |
64 73
|
decnncl |
|
75 |
|
nnrp |
|
76 |
74 75
|
ax-mp |
|
77 |
5 72 76
|
3pm3.2i |
|
78 |
|
logblt |
|
79 |
77 78
|
ax-mp |
|
80 |
68 79
|
mpbi |
|
81 |
80
|
a1i |
|
82 |
|
eqid |
|
83 |
|
2exp5 |
|
84 |
82 83
|
eqtr4i |
|
85 |
84
|
a1i |
|
86 |
85
|
oveq2d |
|
87 |
81 86
|
breqtrd |
|
88 |
|
eqid |
|
89 |
|
3exp3 |
|
90 |
88 89
|
eqtr4i |
|
91 |
90
|
a1i |
|
92 |
91
|
oveq2d |
|
93 |
23 28 52 30
|
relogbzexpd |
|
94 |
92 93
|
eqtrd |
|
95 |
41 56
|
mulcomd |
|
96 |
94 95
|
eqtrd |
|
97 |
|
5re |
|
98 |
97
|
a1i |
|
99 |
98
|
recnd |
|
100 |
51
|
gt0ne0d |
|
101 |
99 41 100
|
divcan1d |
|
102 |
|
5nn |
|
103 |
102
|
a1i |
|
104 |
103
|
nnzd |
|
105 |
23 28 104
|
relogbexpd |
|
106 |
105
|
eqcomd |
|
107 |
101 106
|
eqtrd |
|
108 |
107
|
eqcomd |
|
109 |
87 96 108
|
3brtr3d |
|
110 |
98 40 100
|
redivcld |
|
111 |
55 110 52
|
ltmul1d |
|
112 |
109 111
|
mpbird |
|
113 |
62 112
|
jca |
|
114 |
1 113
|
ax-mp |
|