Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
1
|
rexmet |
|
3 |
|
eqid |
|
4 |
1 3
|
tgioo |
|
5 |
4
|
mopnss |
|
6 |
2 5
|
mpan |
|
7 |
4
|
mopni3 |
|
8 |
7
|
ex |
|
9 |
2 8
|
mp3an1 |
|
10 |
6
|
sselda |
|
11 |
|
rpre |
|
12 |
1
|
bl2ioo |
|
13 |
11 12
|
sylan2 |
|
14 |
13
|
sseq1d |
|
15 |
14
|
anbi2d |
|
16 |
15
|
rexbidva |
|
17 |
16
|
biimpd |
|
18 |
|
rpre |
|
19 |
|
ltle |
|
20 |
11 18 19
|
syl2anr |
|
21 |
20
|
anim1d |
|
22 |
21
|
reximdva |
|
23 |
17 22
|
syl9 |
|
24 |
10 23
|
syl |
|
25 |
9 24
|
mpdd |
|
26 |
25
|
expimpd |
|
27 |
26
|
ralrimivv |
|
28 |
6 27
|
jca |
|
29 |
|
ssel2 |
|
30 |
|
1rp |
|
31 |
|
simpr |
|
32 |
31
|
reximi |
|
33 |
32
|
ralimi |
|
34 |
|
biidd |
|
35 |
34
|
rspcv |
|
36 |
30 33 35
|
mpsyl |
|
37 |
14
|
rexbidva |
|
38 |
36 37
|
syl5ibr |
|
39 |
29 38
|
syl |
|
40 |
39
|
ralimdva |
|
41 |
40
|
imdistani |
|
42 |
4
|
elmopn2 |
|
43 |
2 42
|
ax-mp |
|
44 |
41 43
|
sylibr |
|
45 |
28 44
|
impbii |
|