Step |
Hyp |
Ref |
Expression |
1 |
|
resconn.1 |
|
2 |
|
sconnpconn |
|
3 |
|
pconnconn |
|
4 |
2 3
|
syl |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
5 6
|
rerest |
|
8 |
7 1
|
eqtr4di |
|
9 |
8
|
adantr |
|
10 |
|
simpl |
|
11 |
|
ax-resscn |
|
12 |
10 11
|
sstrdi |
|
13 |
|
df-3an |
|
14 |
|
oveq2 |
|
15 |
|
oveq2 |
|
16 |
14 15
|
oveqan12d |
|
17 |
16
|
eleq1d |
|
18 |
17
|
ralbidv |
|
19 |
|
oveq2 |
|
20 |
|
oveq2 |
|
21 |
19 20
|
oveqan12d |
|
22 |
21
|
eleq1d |
|
23 |
22
|
ralbidv |
|
24 |
|
unitssre |
|
25 |
24 11
|
sstri |
|
26 |
|
simpr |
|
27 |
25 26
|
sseldi |
|
28 |
12
|
adantr |
|
29 |
|
simpr2 |
|
30 |
28 29
|
sseldd |
|
31 |
30
|
adantr |
|
32 |
27 31
|
mulcld |
|
33 |
|
ax-1cn |
|
34 |
|
subcl |
|
35 |
33 27 34
|
sylancr |
|
36 |
|
simpr1 |
|
37 |
28 36
|
sseldd |
|
38 |
37
|
adantr |
|
39 |
35 38
|
mulcld |
|
40 |
32 39
|
addcomd |
|
41 |
|
nncan |
|
42 |
33 27 41
|
sylancr |
|
43 |
42
|
oveq1d |
|
44 |
43
|
oveq2d |
|
45 |
40 44
|
eqtr4d |
|
46 |
|
iirev |
|
47 |
46
|
adantl |
|
48 |
1
|
eleq1i |
|
49 |
|
reconn |
|
50 |
48 49
|
syl5bb |
|
51 |
50
|
biimpa |
|
52 |
51
|
r19.21bi |
|
53 |
52
|
r19.21bi |
|
54 |
53
|
anasss |
|
55 |
54
|
3adantr3 |
|
56 |
55
|
adantr |
|
57 |
|
simpr |
|
58 |
24 57
|
sseldi |
|
59 |
|
simplll |
|
60 |
36
|
adantr |
|
61 |
59 60
|
sseldd |
|
62 |
58 61
|
remulcld |
|
63 |
|
1re |
|
64 |
|
resubcl |
|
65 |
63 58 64
|
sylancr |
|
66 |
29
|
adantr |
|
67 |
59 66
|
sseldd |
|
68 |
65 67
|
remulcld |
|
69 |
62 68
|
readdcld |
|
70 |
58
|
recnd |
|
71 |
|
pncan3 |
|
72 |
70 33 71
|
sylancl |
|
73 |
72
|
oveq1d |
|
74 |
65
|
recnd |
|
75 |
37
|
adantr |
|
76 |
70 74 75
|
adddird |
|
77 |
75
|
mulid2d |
|
78 |
73 76 77
|
3eqtr3d |
|
79 |
65 61
|
remulcld |
|
80 |
|
elicc01 |
|
81 |
57 80
|
sylib |
|
82 |
81
|
simp3d |
|
83 |
|
subge0 |
|
84 |
63 58 83
|
sylancr |
|
85 |
82 84
|
mpbird |
|
86 |
|
simplr3 |
|
87 |
61 67 65 85 86
|
lemul2ad |
|
88 |
79 68 62 87
|
leadd2dd |
|
89 |
78 88
|
eqbrtrrd |
|
90 |
58 67
|
remulcld |
|
91 |
81
|
simp2d |
|
92 |
61 67 58 91 86
|
lemul2ad |
|
93 |
62 90 68 92
|
leadd1dd |
|
94 |
72
|
oveq1d |
|
95 |
30
|
adantr |
|
96 |
70 74 95
|
adddird |
|
97 |
95
|
mulid2d |
|
98 |
94 96 97
|
3eqtr3d |
|
99 |
93 98
|
breqtrd |
|
100 |
|
elicc2 |
|
101 |
61 67 100
|
syl2anc |
|
102 |
69 89 99 101
|
mpbir3and |
|
103 |
56 102
|
sseldd |
|
104 |
103
|
ralrimiva |
|
105 |
104
|
adantr |
|
106 |
|
oveq1 |
|
107 |
|
oveq2 |
|
108 |
107
|
oveq1d |
|
109 |
106 108
|
oveq12d |
|
110 |
109
|
eleq1d |
|
111 |
110
|
rspcv |
|
112 |
47 105 111
|
sylc |
|
113 |
45 112
|
eqeltrd |
|
114 |
113
|
ralrimiva |
|
115 |
|
oveq1 |
|
116 |
|
oveq2 |
|
117 |
116
|
oveq1d |
|
118 |
115 117
|
oveq12d |
|
119 |
118
|
eleq1d |
|
120 |
119
|
cbvralvw |
|
121 |
114 120
|
sylib |
|
122 |
18 23 10 121 104
|
wloglei |
|
123 |
122
|
r19.21bi |
|
124 |
123
|
anasss |
|
125 |
13 124
|
sylan2b |
|
126 |
|
eqid |
|
127 |
12 125 5 126
|
cvxsconn |
|
128 |
9 127
|
eqeltrrd |
|
129 |
128
|
ex |
|
130 |
4 129
|
impbid2 |
|