| Step |
Hyp |
Ref |
Expression |
| 1 |
|
redvabs.d |
|
| 2 |
|
reelprrecn |
|
| 3 |
2
|
a1i |
|
| 4 |
1
|
eleq2i |
|
| 5 |
|
eldifsn |
|
| 6 |
4 5
|
bitri |
|
| 7 |
6
|
simplbi |
|
| 8 |
7
|
recnd |
|
| 9 |
8
|
sqcld |
|
| 10 |
6
|
simprbi |
|
| 11 |
|
sqne0 |
|
| 12 |
8 11
|
syl |
|
| 13 |
10 12
|
mpbird |
|
| 14 |
9 13
|
logcld |
|
| 15 |
14
|
adantl |
|
| 16 |
|
ovexd |
|
| 17 |
|
cnelprrecn |
|
| 18 |
17
|
a1i |
|
| 19 |
|
incom |
|
| 20 |
|
dfrp2 |
|
| 21 |
20
|
ineq2i |
|
| 22 |
|
mnfxr |
|
| 23 |
22
|
a1i |
|
| 24 |
|
0xr |
|
| 25 |
24
|
a1i |
|
| 26 |
|
pnfxr |
|
| 27 |
26
|
a1i |
|
| 28 |
23 25 27
|
iocioodisjd |
|
| 29 |
28
|
mptru |
|
| 30 |
19 21 29
|
3eqtri |
|
| 31 |
|
disjdif2 |
|
| 32 |
30 31
|
ax-mp |
|
| 33 |
|
rpsscn |
|
| 34 |
|
ssdif |
|
| 35 |
33 34
|
ax-mp |
|
| 36 |
32 35
|
eqsstrri |
|
| 37 |
10
|
adantl |
|
| 38 |
|
sqn0rp |
|
| 39 |
7 37 38
|
syl2an2 |
|
| 40 |
36 39
|
sselid |
|
| 41 |
|
ovexd |
|
| 42 |
|
eldifi |
|
| 43 |
|
eldifn |
|
| 44 |
|
mnflt0 |
|
| 45 |
|
0le0 |
|
| 46 |
|
elioc1 |
|
| 47 |
22 24 46
|
mp2an |
|
| 48 |
24 44 45 47
|
mpbir3an |
|
| 49 |
|
eleq1 |
|
| 50 |
48 49
|
mpbiri |
|
| 51 |
50
|
necon3bi |
|
| 52 |
43 51
|
syl |
|
| 53 |
42 52
|
logcld |
|
| 54 |
53
|
adantl |
|
| 55 |
|
ovexd |
|
| 56 |
|
recn |
|
| 57 |
56
|
adantl |
|
| 58 |
57
|
sqcld |
|
| 59 |
|
ovexd |
|
| 60 |
|
eqid |
|
| 61 |
|
cnopn |
|
| 62 |
61
|
a1i |
|
| 63 |
|
ax-resscn |
|
| 64 |
|
dfss2 |
|
| 65 |
63 64
|
mpbi |
|
| 66 |
65
|
a1i |
|
| 67 |
|
sqcl |
|
| 68 |
67
|
adantl |
|
| 69 |
|
ovexd |
|
| 70 |
|
2nn |
|
| 71 |
|
dvexp |
|
| 72 |
70 71
|
mp1i |
|
| 73 |
60 3 62 66 68 69 72
|
dvmptres3 |
|
| 74 |
7
|
ssriv |
|
| 75 |
74
|
a1i |
|
| 76 |
|
tgioo4 |
|
| 77 |
|
rehaus |
|
| 78 |
|
0re |
|
| 79 |
|
uniretop |
|
| 80 |
79
|
sncld |
|
| 81 |
77 78 80
|
mp2an |
|
| 82 |
79
|
cldopn |
|
| 83 |
81 82
|
ax-mp |
|
| 84 |
1 83
|
eqeltri |
|
| 85 |
84
|
a1i |
|
| 86 |
3 58 59 73 75 76 60 85
|
dvmptres |
|
| 87 |
|
2m1e1 |
|
| 88 |
87
|
oveq2i |
|
| 89 |
8
|
exp1d |
|
| 90 |
88 89
|
eqtrid |
|
| 91 |
90
|
oveq2d |
|
| 92 |
91
|
mpteq2ia |
|
| 93 |
86 92
|
eqtrdi |
|
| 94 |
|
logf1o |
|
| 95 |
|
f1of |
|
| 96 |
94 95
|
mp1i |
|
| 97 |
|
snssi |
|
| 98 |
48 97
|
ax-mp |
|
| 99 |
|
sscon |
|
| 100 |
98 99
|
mp1i |
|
| 101 |
96 100
|
feqresmpt |
|
| 102 |
101
|
oveq2d |
|
| 103 |
|
eqid |
|
| 104 |
103
|
dvlog |
|
| 105 |
102 104
|
eqtr3di |
|
| 106 |
|
fveq2 |
|
| 107 |
|
oveq2 |
|
| 108 |
3 18 40 41 54 55 93 105 106 107
|
dvmptco |
|
| 109 |
|
2cnd |
|
| 110 |
|
2ne0 |
|
| 111 |
110
|
a1i |
|
| 112 |
3 15 16 108 109 111
|
dvmptdivc |
|
| 113 |
112
|
mptru |
|
| 114 |
7
|
resqcld |
|
| 115 |
114 13
|
rereccld |
|
| 116 |
115
|
recnd |
|
| 117 |
|
2cnd |
|
| 118 |
116 117 8
|
mul12d |
|
| 119 |
118
|
oveq1d |
|
| 120 |
116 8
|
mulcld |
|
| 121 |
110
|
a1i |
|
| 122 |
120 117 121
|
divcan3d |
|
| 123 |
8
|
sqvald |
|
| 124 |
123
|
oveq2d |
|
| 125 |
124
|
oveq1d |
|
| 126 |
8 8 10 10
|
recdiv2d |
|
| 127 |
126
|
oveq1d |
|
| 128 |
8 10
|
reccld |
|
| 129 |
128 8 10
|
divcan1d |
|
| 130 |
125 127 129
|
3eqtr2d |
|
| 131 |
119 122 130
|
3eqtrd |
|
| 132 |
131
|
mpteq2ia |
|
| 133 |
113 132
|
eqtri |
|