Step |
Hyp |
Ref |
Expression |
1 |
|
exmid |
|
2 |
|
df-ima |
|
3 |
|
df-res |
|
4 |
3
|
rneqi |
|
5 |
2 4
|
eqtri |
|
6 |
|
inxp |
|
7 |
6
|
rneqi |
|
8 |
|
inv1 |
|
9 |
8
|
xpeq2i |
|
10 |
9
|
rneqi |
|
11 |
5 7 10
|
3eqtri |
|
12 |
|
xpeq1 |
|
13 |
|
0xp |
|
14 |
12 13
|
eqtrdi |
|
15 |
14
|
rneqd |
|
16 |
|
rn0 |
|
17 |
15 16
|
eqtrdi |
|
18 |
11 17
|
syl5eq |
|
19 |
18
|
ancli |
|
20 |
|
df-ne |
|
21 |
|
rnxp |
|
22 |
20 21
|
sylbir |
|
23 |
11 22
|
syl5eq |
|
24 |
23
|
ancli |
|
25 |
19 24
|
orim12i |
|
26 |
1 25
|
ax-mp |
|
27 |
|
eqif |
|
28 |
26 27
|
mpbir |
|