Step |
Hyp |
Ref |
Expression |
1 |
|
iooshift.1 |
|
2 |
|
iooshift.2 |
|
3 |
|
iooshift.3 |
|
4 |
|
eqeq1 |
|
5 |
4
|
rexbidv |
|
6 |
5
|
elrab |
|
7 |
|
simprr |
|
8 |
|
nfv |
|
9 |
|
nfv |
|
10 |
|
nfre1 |
|
11 |
9 10
|
nfan |
|
12 |
8 11
|
nfan |
|
13 |
|
nfv |
|
14 |
|
simp3 |
|
15 |
1 3
|
readdcld |
|
16 |
15
|
rexrd |
|
17 |
16
|
adantr |
|
18 |
2 3
|
readdcld |
|
19 |
18
|
rexrd |
|
20 |
19
|
adantr |
|
21 |
|
ioossre |
|
22 |
21
|
a1i |
|
23 |
22
|
sselda |
|
24 |
3
|
adantr |
|
25 |
23 24
|
readdcld |
|
26 |
1
|
adantr |
|
27 |
26
|
rexrd |
|
28 |
2
|
adantr |
|
29 |
28
|
rexrd |
|
30 |
|
simpr |
|
31 |
|
ioogtlb |
|
32 |
27 29 30 31
|
syl3anc |
|
33 |
26 23 24 32
|
ltadd1dd |
|
34 |
|
iooltub |
|
35 |
27 29 30 34
|
syl3anc |
|
36 |
23 28 24 35
|
ltadd1dd |
|
37 |
17 20 25 33 36
|
eliood |
|
38 |
37
|
3adant3 |
|
39 |
14 38
|
eqeltrd |
|
40 |
39
|
3exp |
|
41 |
40
|
adantr |
|
42 |
12 13 41
|
rexlimd |
|
43 |
7 42
|
mpd |
|
44 |
6 43
|
sylan2b |
|
45 |
|
elioore |
|
46 |
45
|
adantl |
|
47 |
46
|
recnd |
|
48 |
1
|
rexrd |
|
49 |
48
|
adantr |
|
50 |
2
|
rexrd |
|
51 |
50
|
adantr |
|
52 |
3
|
adantr |
|
53 |
46 52
|
resubcld |
|
54 |
1
|
recnd |
|
55 |
3
|
recnd |
|
56 |
54 55
|
pncand |
|
57 |
56
|
eqcomd |
|
58 |
57
|
adantr |
|
59 |
15
|
adantr |
|
60 |
16
|
adantr |
|
61 |
19
|
adantr |
|
62 |
|
simpr |
|
63 |
|
ioogtlb |
|
64 |
60 61 62 63
|
syl3anc |
|
65 |
59 46 52 64
|
ltsub1dd |
|
66 |
58 65
|
eqbrtrd |
|
67 |
18
|
adantr |
|
68 |
|
iooltub |
|
69 |
60 61 62 68
|
syl3anc |
|
70 |
46 67 52 69
|
ltsub1dd |
|
71 |
2
|
recnd |
|
72 |
71 55
|
pncand |
|
73 |
72
|
adantr |
|
74 |
70 73
|
breqtrd |
|
75 |
49 51 53 66 74
|
eliood |
|
76 |
55
|
adantr |
|
77 |
47 76
|
npcand |
|
78 |
77
|
eqcomd |
|
79 |
|
oveq1 |
|
80 |
79
|
rspceeqv |
|
81 |
75 78 80
|
syl2anc |
|
82 |
47 81 6
|
sylanbrc |
|
83 |
44 82
|
impbida |
|
84 |
83
|
eqrdv |
|
85 |
84
|
eqcomd |
|