Step |
Hyp |
Ref |
Expression |
1 |
|
zcld.1 |
|
2 |
|
eliun |
|
3 |
|
elioore |
|
4 |
3
|
adantl |
|
5 |
|
eliooord |
|
6 |
|
btwnnz |
|
7 |
6
|
3expb |
|
8 |
5 7
|
sylan2 |
|
9 |
4 8
|
eldifd |
|
10 |
9
|
rexlimiva |
|
11 |
|
eldifi |
|
12 |
11
|
flcld |
|
13 |
12
|
zred |
|
14 |
|
flle |
|
15 |
11 14
|
syl |
|
16 |
|
eldifn |
|
17 |
|
nelne2 |
|
18 |
12 16 17
|
syl2anc |
|
19 |
18
|
necomd |
|
20 |
13 11 15 19
|
leneltd |
|
21 |
|
flltp1 |
|
22 |
11 21
|
syl |
|
23 |
13
|
rexrd |
|
24 |
|
peano2re |
|
25 |
13 24
|
syl |
|
26 |
25
|
rexrd |
|
27 |
|
elioo2 |
|
28 |
23 26 27
|
syl2anc |
|
29 |
11 20 22 28
|
mpbir3and |
|
30 |
|
id |
|
31 |
|
oveq1 |
|
32 |
30 31
|
oveq12d |
|
33 |
32
|
eleq2d |
|
34 |
33
|
rspcev |
|
35 |
12 29 34
|
syl2anc |
|
36 |
10 35
|
impbii |
|
37 |
2 36
|
bitri |
|
38 |
37
|
eqriv |
|
39 |
|
retop |
|
40 |
1 39
|
eqeltri |
|
41 |
|
iooretop |
|
42 |
41 1
|
eleqtrri |
|
43 |
42
|
rgenw |
|
44 |
|
iunopn |
|
45 |
40 43 44
|
mp2an |
|
46 |
38 45
|
eqeltrri |
|
47 |
|
zssre |
|
48 |
|
uniretop |
|
49 |
1
|
unieqi |
|
50 |
48 49
|
eqtr4i |
|
51 |
50
|
iscld2 |
|
52 |
40 47 51
|
mp2an |
|
53 |
46 52
|
mpbir |
|