Step |
Hyp |
Ref |
Expression |
1 |
|
fveqdmss.1 |
|
2 |
1
|
fveqdmss |
|
3 |
|
dmres |
|
4 |
|
incom |
|
5 |
|
sseqin2 |
|
6 |
5
|
biimpi |
|
7 |
4 6
|
eqtrid |
|
8 |
3 7
|
eqtrid |
|
9 |
8 1
|
eqtrdi |
|
10 |
2 9
|
syl |
|
11 |
|
fvres |
|
12 |
11
|
adantl |
|
13 |
|
id |
|
14 |
12 13
|
sylan9eq |
|
15 |
14
|
ex |
|
16 |
15
|
ralimdva |
|
17 |
16
|
3impia |
|
18 |
2 7
|
syl |
|
19 |
3 18
|
eqtrid |
|
20 |
17 19
|
raleqtrrdv |
|
21 |
|
simpll |
|
22 |
1
|
eleq2i |
|
23 |
22
|
biimpi |
|
24 |
23
|
adantl |
|
25 |
|
simplr |
|
26 |
|
nelrnfvne |
|
27 |
21 24 25 26
|
syl3anc |
|
28 |
|
neeq1 |
|
29 |
27 28
|
syl5ibrcom |
|
30 |
29
|
ralimdva |
|
31 |
30
|
3impia |
|
32 |
|
fvn0ssdmfun |
|
33 |
32
|
simprd |
|
34 |
31 33
|
syl |
|
35 |
|
simp1 |
|
36 |
|
eqfunfv |
|
37 |
34 35 36
|
syl2anc |
|
38 |
10 20 37
|
mpbir2and |
|