Step |
Hyp |
Ref |
Expression |
1 |
|
kqval.2 |
|
2 |
|
imadmres |
|
3 |
|
dmres |
|
4 |
1
|
kqffn |
|
5 |
4
|
adantr |
|
6 |
5
|
fndmd |
|
7 |
6
|
ineq2d |
|
8 |
3 7
|
syl5eq |
|
9 |
8
|
imaeq2d |
|
10 |
2 9
|
syl5eqr |
|
11 |
|
indif1 |
|
12 |
|
inss2 |
|
13 |
|
ssdif |
|
14 |
12 13
|
ax-mp |
|
15 |
11 14
|
eqsstri |
|
16 |
|
imass2 |
|
17 |
15 16
|
mp1i |
|
18 |
10 17
|
eqsstrd |
|
19 |
|
sslin |
|
20 |
18 19
|
syl |
|
21 |
|
eldifn |
|
22 |
21
|
adantl |
|
23 |
|
simpll |
|
24 |
|
simplr |
|
25 |
|
eldifi |
|
26 |
25
|
adantl |
|
27 |
1
|
kqfvima |
|
28 |
23 24 26 27
|
syl3anc |
|
29 |
22 28
|
mtbid |
|
30 |
29
|
ralrimiva |
|
31 |
|
difss |
|
32 |
|
eleq1 |
|
33 |
32
|
notbid |
|
34 |
33
|
ralima |
|
35 |
5 31 34
|
sylancl |
|
36 |
30 35
|
mpbird |
|
37 |
|
disjr |
|
38 |
36 37
|
sylibr |
|
39 |
|
sseq0 |
|
40 |
20 38 39
|
syl2anc |
|