Step |
Hyp |
Ref |
Expression |
1 |
|
simp3 |
|
2 |
|
dfss3 |
|
3 |
|
fvelrnb |
|
4 |
3
|
ralbidv |
|
5 |
2 4
|
syl5bb |
|
6 |
5
|
biimpa |
|
7 |
6
|
3adant3 |
|
8 |
|
fveqeq2 |
|
9 |
8
|
ac6sfi |
|
10 |
1 7 9
|
syl2anc |
|
11 |
|
fimass |
|
12 |
|
vex |
|
13 |
12
|
imaex |
|
14 |
13
|
elpw |
|
15 |
11 14
|
sylibr |
|
16 |
15
|
ad2antrl |
|
17 |
|
ffun |
|
18 |
17
|
ad2antrl |
|
19 |
|
simpl3 |
|
20 |
|
imafi |
|
21 |
18 19 20
|
syl2anc |
|
22 |
16 21
|
elind |
|
23 |
|
fvco3 |
|
24 |
|
fvresi |
|
25 |
24
|
adantl |
|
26 |
23 25
|
eqeq12d |
|
27 |
26
|
ralbidva |
|
28 |
27
|
biimprd |
|
29 |
28
|
adantl |
|
30 |
29
|
impr |
|
31 |
|
simpl1 |
|
32 |
|
ffn |
|
33 |
32
|
ad2antrl |
|
34 |
|
frn |
|
35 |
34
|
ad2antrl |
|
36 |
|
fnco |
|
37 |
31 33 35 36
|
syl3anc |
|
38 |
|
fnresi |
|
39 |
|
eqfnfv |
|
40 |
37 38 39
|
sylancl |
|
41 |
30 40
|
mpbird |
|
42 |
41
|
imaeq1d |
|
43 |
|
imaco |
|
44 |
|
ssid |
|
45 |
|
resiima |
|
46 |
44 45
|
ax-mp |
|
47 |
42 43 46
|
3eqtr3g |
|
48 |
|
imaeq2 |
|
49 |
48
|
eqeq1d |
|
50 |
49
|
rspcev |
|
51 |
22 47 50
|
syl2anc |
|
52 |
10 51
|
exlimddv |
|