Step |
Hyp |
Ref |
Expression |
1 |
|
simpl |
|
2 |
|
vex |
|
3 |
2
|
a1i |
|
4 |
|
df-br |
|
5 |
4
|
biimpri |
|
6 |
5
|
adantl |
|
7 |
|
breldmg |
|
8 |
1 3 6 7
|
syl3anc |
|
9 |
|
simpl |
|
10 |
|
velsn |
|
11 |
|
breq1 |
|
12 |
4 11
|
bitr3id |
|
13 |
12
|
eqcoms |
|
14 |
13
|
eubidv |
|
15 |
14
|
biimpd |
|
16 |
10 15
|
sylbi |
|
17 |
16
|
com12 |
|
18 |
17
|
adantl |
|
19 |
18
|
ralrimiv |
|
20 |
|
fnres |
|
21 |
|
fnfun |
|
22 |
20 21
|
sylbir |
|
23 |
19 22
|
syl |
|
24 |
9 23
|
jca |
|
25 |
24
|
ex |
|
26 |
8 25
|
syl |
|
27 |
26
|
impr |
|
28 |
|
df-dfat |
|
29 |
27 28
|
sylibr |
|
30 |
|
dfatafv2iota |
|
31 |
29 30
|
syl |
|
32 |
4
|
bicomi |
|
33 |
32
|
eubii |
|
34 |
33
|
biimpi |
|
35 |
5 34
|
anim12i |
|
36 |
35
|
adantl |
|
37 |
|
iota1 |
|
38 |
37
|
biimpac |
|
39 |
36 38
|
syl |
|
40 |
31 39
|
eqtrd |
|
41 |
40
|
ex |
|
42 |
|
eu2ndop1stv |
|
43 |
42
|
pm2.24d |
|
44 |
43
|
adantl |
|
45 |
44
|
com12 |
|
46 |
41 45
|
pm2.61i |
|