Step |
Hyp |
Ref |
Expression |
1 |
|
sepfsepc.1 |
|
2 |
|
simpl |
|
3 |
|
0re |
|
4 |
|
1re |
|
5 |
|
0le0 |
|
6 |
|
3re |
|
7 |
|
3ne0 |
|
8 |
6 7
|
rereccli |
|
9 |
|
1lt3 |
|
10 |
|
recgt1i |
|
11 |
6 9 10
|
mp2an |
|
12 |
11
|
simpri |
|
13 |
8 4 12
|
ltleii |
|
14 |
|
iccss |
|
15 |
3 4 5 13 14
|
mp4an |
|
16 |
|
i0oii |
|
17 |
13 16
|
ax-mp |
|
18 |
11
|
simpli |
|
19 |
8
|
rexri |
|
20 |
|
elico2 |
|
21 |
3 19 20
|
mp2an |
|
22 |
21
|
biimpri |
|
23 |
22
|
snssd |
|
24 |
3 5 18 23
|
mp3an |
|
25 |
|
icossicc |
|
26 |
24 25
|
pm3.2i |
|
27 |
|
sseq2 |
|
28 |
|
sseq1 |
|
29 |
27 28
|
anbi12d |
|
30 |
29
|
rspcev |
|
31 |
17 26 30
|
mp2an |
|
32 |
|
iitop |
|
33 |
24 25
|
sstri |
|
34 |
33 15
|
sstri |
|
35 |
|
iiuni |
|
36 |
35
|
isnei |
|
37 |
32 34 36
|
mp2an |
|
38 |
15 31 37
|
mpbir2an |
|
39 |
38
|
a1i |
|
40 |
|
simprl |
|
41 |
2 39 40
|
cnneiima |
|
42 |
|
halfge0 |
|
43 |
|
1le1 |
|
44 |
|
iccss |
|
45 |
3 4 42 43 44
|
mp4an |
|
46 |
|
io1ii |
|
47 |
42 46
|
ax-mp |
|
48 |
|
halflt1 |
|
49 |
|
halfre |
|
50 |
49
|
rexri |
|
51 |
|
elioc2 |
|
52 |
50 4 51
|
mp2an |
|
53 |
52
|
biimpri |
|
54 |
53
|
snssd |
|
55 |
4 48 43 54
|
mp3an |
|
56 |
|
iocssicc |
|
57 |
55 56
|
pm3.2i |
|
58 |
|
sseq2 |
|
59 |
|
sseq1 |
|
60 |
58 59
|
anbi12d |
|
61 |
60
|
rspcev |
|
62 |
47 57 61
|
mp2an |
|
63 |
55 56
|
sstri |
|
64 |
63 45
|
sstri |
|
65 |
35
|
isnei |
|
66 |
32 64 65
|
mp2an |
|
67 |
45 62 66
|
mpbir2an |
|
68 |
67
|
a1i |
|
69 |
|
simprr |
|
70 |
2 68 69
|
cnneiima |
|
71 |
|
icccldii |
|
72 |
5 13 71
|
mp2an |
|
73 |
|
cnclima |
|
74 |
2 72 73
|
sylancl |
|
75 |
|
icccldii |
|
76 |
42 43 75
|
mp2an |
|
77 |
|
cnclima |
|
78 |
2 76 77
|
sylancl |
|
79 |
|
eqid |
|
80 |
79 35
|
cnf |
|
81 |
80
|
ffund |
|
82 |
2 81
|
syl |
|
83 |
|
0xr |
|
84 |
|
1xr |
|
85 |
|
2lt3 |
|
86 |
|
2re |
|
87 |
|
2pos |
|
88 |
|
3pos |
|
89 |
86 6 87 88
|
ltrecii |
|
90 |
85 89
|
mpbi |
|
91 |
|
iccdisj2 |
|
92 |
83 84 90 91
|
mp3an |
|
93 |
92
|
a1i |
|
94 |
|
ssidd |
|
95 |
|
ssidd |
|
96 |
82 93 94 95
|
predisj |
|
97 |
|
eleq1 |
|
98 |
|
ineq1 |
|
99 |
98
|
eqeq1d |
|
100 |
97 99
|
3anbi13d |
|
101 |
|
eleq1 |
|
102 |
|
ineq2 |
|
103 |
102
|
eqeq1d |
|
104 |
101 103
|
3anbi23d |
|
105 |
100 104
|
rspc2ev |
|
106 |
41 70 74 78 96 105
|
syl113anc |
|
107 |
106
|
rexlimiva |
|
108 |
1 107
|
syl |
|