Step |
Hyp |
Ref |
Expression |
1 |
|
ioorf.1 |
|
2 |
|
ioof |
|
3 |
|
ffn |
|
4 |
|
ovelrn |
|
5 |
2 3 4
|
mp2b |
|
6 |
1
|
ioorinv2 |
|
7 |
6
|
fveq2d |
|
8 |
|
df-ov |
|
9 |
7 8
|
eqtr4di |
|
10 |
|
df-ne |
|
11 |
|
neeq1 |
|
12 |
10 11
|
bitr3id |
|
13 |
|
2fveq3 |
|
14 |
|
id |
|
15 |
13 14
|
eqeq12d |
|
16 |
12 15
|
imbi12d |
|
17 |
9 16
|
mpbiri |
|
18 |
17
|
a1i |
|
19 |
18
|
rexlimivv |
|
20 |
5 19
|
sylbi |
|
21 |
|
ioorebas |
|
22 |
1
|
ioorval |
|
23 |
21 22
|
ax-mp |
|
24 |
|
iooid |
|
25 |
24
|
iftruei |
|
26 |
23 25
|
eqtri |
|
27 |
26
|
fveq2i |
|
28 |
|
df-ov |
|
29 |
27 28
|
eqtr4i |
|
30 |
24
|
eqeq2i |
|
31 |
30
|
biimpri |
|
32 |
31
|
fveq2d |
|
33 |
32
|
fveq2d |
|
34 |
29 33 31
|
3eqtr4a |
|
35 |
20 34
|
pm2.61d2 |
|