Step |
Hyp |
Ref |
Expression |
1 |
|
2re |
|
2 |
|
simp1 |
|
3 |
|
remulcl |
|
4 |
1 2 3
|
sylancr |
|
5 |
|
simp3 |
|
6 |
|
1re |
|
7 |
|
simp2 |
|
8 |
|
difrp |
|
9 |
6 7 8
|
sylancr |
|
10 |
5 9
|
mpbid |
|
11 |
4 10
|
rerpdivcld |
|
12 |
|
expnbnd |
|
13 |
11 7 5 12
|
syl3anc |
|
14 |
|
2nn0 |
|
15 |
|
nnnn0 |
|
16 |
15
|
ad2antrl |
|
17 |
|
nn0mulcl |
|
18 |
14 16 17
|
sylancr |
|
19 |
2
|
ad2antrr |
|
20 |
|
2nn |
|
21 |
|
simprl |
|
22 |
|
nnmulcl |
|
23 |
20 21 22
|
sylancr |
|
24 |
|
eluznn |
|
25 |
23 24
|
sylan |
|
26 |
25
|
nnred |
|
27 |
19 26
|
remulcld |
|
28 |
|
0re |
|
29 |
|
ifcl |
|
30 |
19 28 29
|
sylancl |
|
31 |
|
remulcl |
|
32 |
1 30 31
|
sylancr |
|
33 |
|
simplrl |
|
34 |
33
|
nnred |
|
35 |
26 34
|
resubcld |
|
36 |
32 35
|
remulcld |
|
37 |
7
|
ad2antrr |
|
38 |
25
|
nnnn0d |
|
39 |
|
reexpcl |
|
40 |
37 38 39
|
syl2anc |
|
41 |
|
remulcl |
|
42 |
1 35 41
|
sylancr |
|
43 |
38
|
nn0ge0d |
|
44 |
|
max1 |
|
45 |
28 19 44
|
sylancr |
|
46 |
|
remulcl |
|
47 |
1 34 46
|
sylancr |
|
48 |
|
eluzle |
|
49 |
48
|
adantl |
|
50 |
47 26 26 49
|
leadd2dd |
|
51 |
26
|
recnd |
|
52 |
51
|
2timesd |
|
53 |
50 52
|
breqtrrd |
|
54 |
|
remulcl |
|
55 |
1 26 54
|
sylancr |
|
56 |
|
leaddsub |
|
57 |
26 47 55 56
|
syl3anc |
|
58 |
53 57
|
mpbid |
|
59 |
|
2cnd |
|
60 |
34
|
recnd |
|
61 |
59 51 60
|
subdid |
|
62 |
58 61
|
breqtrrd |
|
63 |
|
max2 |
|
64 |
28 19 63
|
sylancr |
|
65 |
26 42 19 30 43 45 62 64
|
lemul12bd |
|
66 |
19
|
recnd |
|
67 |
66 51
|
mulcomd |
|
68 |
30
|
recnd |
|
69 |
35
|
recnd |
|
70 |
59 68 69
|
mul32d |
|
71 |
65 67 70
|
3brtr4d |
|
72 |
10
|
ad2antrr |
|
73 |
72
|
rpred |
|
74 |
73 35
|
remulcld |
|
75 |
33
|
nnnn0d |
|
76 |
|
reexpcl |
|
77 |
37 75 76
|
syl2anc |
|
78 |
74 77
|
remulcld |
|
79 |
|
simplrr |
|
80 |
1 19 3
|
sylancr |
|
81 |
80 77 72
|
ltdivmuld |
|
82 |
79 81
|
mpbid |
|
83 |
5
|
ad2antrr |
|
84 |
|
posdif |
|
85 |
6 37 84
|
sylancr |
|
86 |
83 85
|
mpbid |
|
87 |
33
|
nnzd |
|
88 |
28
|
a1i |
|
89 |
6
|
a1i |
|
90 |
|
0lt1 |
|
91 |
90
|
a1i |
|
92 |
88 89 37 91 83
|
lttrd |
|
93 |
|
expgt0 |
|
94 |
37 87 92 93
|
syl3anc |
|
95 |
73 77 86 94
|
mulgt0d |
|
96 |
|
oveq2 |
|
97 |
96
|
breq1d |
|
98 |
|
2t0e0 |
|
99 |
|
oveq2 |
|
100 |
98 99
|
syl5eqr |
|
101 |
100
|
breq1d |
|
102 |
97 101
|
ifboth |
|
103 |
82 95 102
|
syl2anc |
|
104 |
73 77
|
remulcld |
|
105 |
|
simpr |
|
106 |
60
|
2timesd |
|
107 |
106
|
fveq2d |
|
108 |
105 107
|
eleqtrd |
|
109 |
|
eluzsub |
|
110 |
87 87 108 109
|
syl3anc |
|
111 |
|
eluznn |
|
112 |
33 110 111
|
syl2anc |
|
113 |
112
|
nngt0d |
|
114 |
|
ltmul1 |
|
115 |
32 104 35 113 114
|
syl112anc |
|
116 |
103 115
|
mpbid |
|
117 |
73
|
recnd |
|
118 |
77
|
recnd |
|
119 |
117 118 69
|
mul32d |
|
120 |
116 119
|
breqtrd |
|
121 |
|
peano2re |
|
122 |
74 121
|
syl |
|
123 |
112
|
nnnn0d |
|
124 |
|
reexpcl |
|
125 |
37 123 124
|
syl2anc |
|
126 |
74
|
ltp1d |
|
127 |
88 37 92
|
ltled |
|
128 |
|
bernneq2 |
|
129 |
37 123 127 128
|
syl3anc |
|
130 |
74 122 125 126 129
|
ltletrd |
|
131 |
37
|
recnd |
|
132 |
92
|
gt0ne0d |
|
133 |
|
eluzelz |
|
134 |
133
|
adantl |
|
135 |
|
expsub |
|
136 |
131 132 134 87 135
|
syl22anc |
|
137 |
130 136
|
breqtrd |
|
138 |
|
ltmuldiv |
|
139 |
74 40 77 94 138
|
syl112anc |
|
140 |
137 139
|
mpbird |
|
141 |
36 78 40 120 140
|
lttrd |
|
142 |
27 36 40 71 141
|
lelttrd |
|
143 |
142
|
ralrimiva |
|
144 |
|
fveq2 |
|
145 |
144
|
raleqdv |
|
146 |
145
|
rspcev |
|
147 |
18 143 146
|
syl2anc |
|
148 |
13 147
|
rexlimddv |
|