Step |
Hyp |
Ref |
Expression |
1 |
|
dvbdfbdioolem1.a |
|
2 |
|
dvbdfbdioolem1.b |
|
3 |
|
dvbdfbdioolem1.f |
|
4 |
|
dvbdfbdioolem1.dmdv |
|
5 |
|
dvbdfbdioolem1.k |
|
6 |
|
dvbdfbdioolem1.dvbd |
|
7 |
|
dvbdfbdioolem1.c |
|
8 |
|
dvbdfbdioolem1.d |
|
9 |
|
ioossre |
|
10 |
9 7
|
sseldi |
|
11 |
|
ioossre |
|
12 |
11 8
|
sseldi |
|
13 |
10
|
rexrd |
|
14 |
2
|
rexrd |
|
15 |
|
ioogtlb |
|
16 |
13 14 8 15
|
syl3anc |
|
17 |
1
|
rexrd |
|
18 |
|
ioogtlb |
|
19 |
17 14 7 18
|
syl3anc |
|
20 |
|
iooltub |
|
21 |
13 14 8 20
|
syl3anc |
|
22 |
|
iccssioo |
|
23 |
17 14 19 21 22
|
syl22anc |
|
24 |
|
ax-resscn |
|
25 |
24
|
a1i |
|
26 |
3 25
|
fssd |
|
27 |
9
|
a1i |
|
28 |
|
dvcn |
|
29 |
25 26 27 4 28
|
syl31anc |
|
30 |
|
cncffvrn |
|
31 |
25 29 30
|
syl2anc |
|
32 |
3 31
|
mpbird |
|
33 |
|
rescncf |
|
34 |
23 32 33
|
sylc |
|
35 |
23 27
|
sstrd |
|
36 |
|
eqid |
|
37 |
36
|
tgioo2 |
|
38 |
36 37
|
dvres |
|
39 |
25 26 27 35 38
|
syl22anc |
|
40 |
|
iccntr |
|
41 |
10 12 40
|
syl2anc |
|
42 |
41
|
reseq2d |
|
43 |
39 42
|
eqtrd |
|
44 |
43
|
dmeqd |
|
45 |
1 10 19
|
ltled |
|
46 |
12 2 21
|
ltled |
|
47 |
|
ioossioo |
|
48 |
17 14 45 46 47
|
syl22anc |
|
49 |
48 4
|
sseqtrrd |
|
50 |
|
ssdmres |
|
51 |
49 50
|
sylib |
|
52 |
44 51
|
eqtrd |
|
53 |
10 12 16 34 52
|
mvth |
|
54 |
43
|
fveq1d |
|
55 |
|
fvres |
|
56 |
54 55
|
sylan9eq |
|
57 |
56
|
eqcomd |
|
58 |
57
|
3adant3 |
|
59 |
|
simp3 |
|
60 |
12
|
rexrd |
|
61 |
10 12 16
|
ltled |
|
62 |
|
ubicc2 |
|
63 |
13 60 61 62
|
syl3anc |
|
64 |
|
fvres |
|
65 |
63 64
|
syl |
|
66 |
|
lbicc2 |
|
67 |
13 60 61 66
|
syl3anc |
|
68 |
|
fvres |
|
69 |
67 68
|
syl |
|
70 |
65 69
|
oveq12d |
|
71 |
70
|
oveq1d |
|
72 |
71
|
3ad2ant1 |
|
73 |
58 59 72
|
3eqtrd |
|
74 |
|
simp3 |
|
75 |
74
|
eqcomd |
|
76 |
23 63
|
sseldd |
|
77 |
3 76
|
ffvelrnd |
|
78 |
3 7
|
ffvelrnd |
|
79 |
77 78
|
resubcld |
|
80 |
79
|
recnd |
|
81 |
80
|
3ad2ant1 |
|
82 |
|
dvfre |
|
83 |
3 27 82
|
syl2anc |
|
84 |
4
|
feq2d |
|
85 |
83 84
|
mpbid |
|
86 |
85
|
adantr |
|
87 |
48
|
sselda |
|
88 |
86 87
|
ffvelrnd |
|
89 |
88
|
recnd |
|
90 |
89
|
3adant3 |
|
91 |
12 10
|
resubcld |
|
92 |
91
|
recnd |
|
93 |
92
|
3ad2ant1 |
|
94 |
10 12
|
posdifd |
|
95 |
16 94
|
mpbid |
|
96 |
95
|
gt0ne0d |
|
97 |
96
|
3ad2ant1 |
|
98 |
81 90 93 97
|
divmul3d |
|
99 |
75 98
|
mpbid |
|
100 |
99
|
fveq2d |
|
101 |
92
|
adantr |
|
102 |
89 101
|
absmuld |
|
103 |
102
|
3adant3 |
|
104 |
100 103
|
eqtrd |
|
105 |
10 12 61
|
abssubge0d |
|
106 |
105
|
oveq2d |
|
107 |
106
|
3ad2ant1 |
|
108 |
104 107
|
eqtrd |
|
109 |
89
|
abscld |
|
110 |
5
|
adantr |
|
111 |
91
|
adantr |
|
112 |
|
0red |
|
113 |
112 91 95
|
ltled |
|
114 |
113
|
adantr |
|
115 |
6
|
adantr |
|
116 |
|
rspa |
|
117 |
115 87 116
|
syl2anc |
|
118 |
109 110 111 114 117
|
lemul1ad |
|
119 |
118
|
3adant3 |
|
120 |
108 119
|
eqbrtrd |
|
121 |
73 120
|
syld3an3 |
|
122 |
101
|
abscld |
|
123 |
2 1
|
resubcld |
|
124 |
123
|
adantr |
|
125 |
89
|
absge0d |
|
126 |
101
|
absge0d |
|
127 |
12 1 2 10 46 45
|
le2subd |
|
128 |
105 127
|
eqbrtrd |
|
129 |
128
|
adantr |
|
130 |
109 110 122 124 125 126 117 129
|
lemul12ad |
|
131 |
130
|
3adant3 |
|
132 |
104 131
|
eqbrtrd |
|
133 |
73 132
|
syld3an3 |
|
134 |
121 133
|
jca |
|
135 |
134
|
rexlimdv3a |
|
136 |
53 135
|
mpd |
|