Step |
Hyp |
Ref |
Expression |
1 |
|
remet.1 |
|
2 |
1
|
rexmet |
|
3 |
|
blrn |
|
4 |
2 3
|
ax-mp |
|
5 |
|
elxr |
|
6 |
1
|
bl2ioo |
|
7 |
|
resubcl |
|
8 |
|
readdcl |
|
9 |
|
ioof |
|
10 |
|
ffn |
|
11 |
9 10
|
ax-mp |
|
12 |
|
rexr |
|
13 |
|
rexr |
|
14 |
|
fnovrn |
|
15 |
11 12 13 14
|
mp3an3an |
|
16 |
7 8 15
|
syl2anc |
|
17 |
6 16
|
eqeltrd |
|
18 |
|
oveq2 |
|
19 |
1
|
remet |
|
20 |
|
blpnf |
|
21 |
19 20
|
mpan |
|
22 |
18 21
|
sylan9eqr |
|
23 |
|
ioomax |
|
24 |
|
ioorebas |
|
25 |
23 24
|
eqeltrri |
|
26 |
22 25
|
eqeltrdi |
|
27 |
|
oveq2 |
|
28 |
|
0xr |
|
29 |
|
nltmnf |
|
30 |
28 29
|
ax-mp |
|
31 |
|
mnfxr |
|
32 |
|
xbln0 |
|
33 |
2 31 32
|
mp3an13 |
|
34 |
33
|
necon1bbid |
|
35 |
30 34
|
mpbii |
|
36 |
27 35
|
sylan9eqr |
|
37 |
|
iooid |
|
38 |
|
ioorebas |
|
39 |
37 38
|
eqeltrri |
|
40 |
36 39
|
eqeltrdi |
|
41 |
17 26 40
|
3jaodan |
|
42 |
5 41
|
sylan2b |
|
43 |
|
eleq1 |
|
44 |
42 43
|
syl5ibrcom |
|
45 |
44
|
rexlimivv |
|
46 |
4 45
|
sylbi |
|
47 |
46
|
ssriv |
|