Step |
Hyp |
Ref |
Expression |
1 |
|
cnheibor.2 |
|
2 |
|
cnheibor.3 |
|
3 |
1
|
cnfldhaus |
|
4 |
|
simpl |
|
5 |
|
simpr |
|
6 |
2 5
|
eqeltrrid |
|
7 |
1
|
cnfldtopon |
|
8 |
7
|
toponunii |
|
9 |
8
|
hauscmp |
|
10 |
3 4 6 9
|
mp3an2i |
|
11 |
1
|
cnfldtop |
|
12 |
8
|
restuni |
|
13 |
11 4 12
|
sylancr |
|
14 |
2
|
unieqi |
|
15 |
13 14
|
eqtr4di |
|
16 |
15
|
eleq2d |
|
17 |
16
|
biimpar |
|
18 |
|
cnex |
|
19 |
|
ssexg |
|
20 |
4 18 19
|
sylancl |
|
21 |
20
|
adantr |
|
22 |
|
cnxmet |
|
23 |
|
0cnd |
|
24 |
4
|
sselda |
|
25 |
24
|
abscld |
|
26 |
|
peano2re |
|
27 |
25 26
|
syl |
|
28 |
27
|
rexrd |
|
29 |
1
|
cnfldtopn |
|
30 |
29
|
blopn |
|
31 |
22 23 28 30
|
mp3an2i |
|
32 |
|
elrestr |
|
33 |
11 21 31 32
|
mp3an2i |
|
34 |
33 2
|
eleqtrrdi |
|
35 |
|
0cn |
|
36 |
|
eqid |
|
37 |
36
|
cnmetdval |
|
38 |
35 37
|
mpan |
|
39 |
|
df-neg |
|
40 |
39
|
fveq2i |
|
41 |
|
absneg |
|
42 |
40 41
|
eqtr3id |
|
43 |
38 42
|
eqtrd |
|
44 |
24 43
|
syl |
|
45 |
25
|
ltp1d |
|
46 |
44 45
|
eqbrtrd |
|
47 |
|
elbl |
|
48 |
22 23 28 47
|
mp3an2i |
|
49 |
24 46 48
|
mpbir2and |
|
50 |
|
simpr |
|
51 |
49 50
|
elind |
|
52 |
24
|
absge0d |
|
53 |
25 52
|
ge0p1rpd |
|
54 |
|
eqid |
|
55 |
|
oveq2 |
|
56 |
55
|
ineq1d |
|
57 |
56
|
rspceeqv |
|
58 |
53 54 57
|
sylancl |
|
59 |
|
eleq2 |
|
60 |
|
eqeq1 |
|
61 |
60
|
rexbidv |
|
62 |
59 61
|
anbi12d |
|
63 |
62
|
rspcev |
|
64 |
34 51 58 63
|
syl12anc |
|
65 |
17 64
|
syldan |
|
66 |
65
|
ralrimiva |
|
67 |
|
eqid |
|
68 |
|
oveq2 |
|
69 |
68
|
ineq1d |
|
70 |
69
|
eqeq2d |
|
71 |
67 70
|
cmpcovf |
|
72 |
5 66 71
|
syl2anc |
|
73 |
15
|
ad4antr |
|
74 |
|
simpllr |
|
75 |
73 74
|
eqtrd |
|
76 |
75
|
eleq2d |
|
77 |
|
eluni2 |
|
78 |
76 77
|
bitrdi |
|
79 |
|
elssuni |
|
80 |
79
|
ad2antrl |
|
81 |
75
|
adantr |
|
82 |
80 81
|
sseqtrrd |
|
83 |
|
simp-6l |
|
84 |
82 83
|
sstrd |
|
85 |
|
simprr |
|
86 |
84 85
|
sseldd |
|
87 |
86
|
abscld |
|
88 |
|
simplrl |
|
89 |
|
simprl |
|
90 |
89
|
ad2antrr |
|
91 |
|
simprl |
|
92 |
90 91
|
ffvelrnd |
|
93 |
92
|
rpred |
|
94 |
86 43
|
syl |
|
95 |
|
id |
|
96 |
|
fveq2 |
|
97 |
96
|
oveq2d |
|
98 |
97
|
ineq1d |
|
99 |
95 98
|
eqeq12d |
|
100 |
|
simprr |
|
101 |
100
|
ad2antrr |
|
102 |
99 101 91
|
rspcdva |
|
103 |
85 102
|
eleqtrd |
|
104 |
103
|
elin1d |
|
105 |
|
0cnd |
|
106 |
92
|
rpxrd |
|
107 |
|
elbl |
|
108 |
22 105 106 107
|
mp3an2i |
|
109 |
104 108
|
mpbid |
|
110 |
109
|
simprd |
|
111 |
94 110
|
eqbrtrrd |
|
112 |
96
|
breq1d |
|
113 |
|
simplrr |
|
114 |
112 113 91
|
rspcdva |
|
115 |
87 93 88 111 114
|
ltletrd |
|
116 |
87 88 115
|
ltled |
|
117 |
116
|
rexlimdvaa |
|
118 |
78 117
|
sylbid |
|
119 |
118
|
ralrimiv |
|
120 |
|
simpllr |
|
121 |
120
|
elin2d |
|
122 |
|
ffvelrn |
|
123 |
122
|
rpred |
|
124 |
123
|
ralrimiva |
|
125 |
124
|
ad2antrl |
|
126 |
|
fimaxre3 |
|
127 |
121 125 126
|
syl2anc |
|
128 |
119 127
|
reximddv |
|
129 |
128
|
ex |
|
130 |
129
|
exlimdv |
|
131 |
130
|
expimpd |
|
132 |
131
|
rexlimdva |
|
133 |
72 132
|
mpd |
|
134 |
10 133
|
jca |
|
135 |
|
eqid |
|
136 |
|
eqid |
|
137 |
1 2 135 136
|
cnheiborlem |
|
138 |
137
|
rexlimdvaa |
|
139 |
138
|
imp |
|
140 |
139
|
adantl |
|
141 |
134 140
|
impbida |
|