Step |
Hyp |
Ref |
Expression |
1 |
|
n0 |
|
2 |
|
uniiun |
|
3 |
|
simpl1 |
|
4 |
|
toponmax |
|
5 |
3 4
|
syl |
|
6 |
|
simpl2l |
|
7 |
5 6
|
ssexd |
|
8 |
|
simpl2r |
|
9 |
5 8
|
ssexd |
|
10 |
|
uniprg |
|
11 |
7 9 10
|
syl2anc |
|
12 |
2 11
|
syl5eqr |
|
13 |
12
|
oveq2d |
|
14 |
|
vex |
|
15 |
14
|
elpr |
|
16 |
|
simpl2 |
|
17 |
|
sseq1 |
|
18 |
17
|
biimprd |
|
19 |
|
sseq1 |
|
20 |
19
|
biimprd |
|
21 |
18 20
|
jaoa |
|
22 |
16 21
|
mpan9 |
|
23 |
15 22
|
sylan2b |
|
24 |
|
simpl3 |
|
25 |
|
elin |
|
26 |
24 25
|
sylib |
|
27 |
|
eleq2 |
|
28 |
27
|
biimprd |
|
29 |
|
eleq2 |
|
30 |
29
|
biimprd |
|
31 |
28 30
|
jaoa |
|
32 |
26 31
|
mpan9 |
|
33 |
15 32
|
sylan2b |
|
34 |
|
simpr |
|
35 |
|
oveq2 |
|
36 |
35
|
eleq1d |
|
37 |
36
|
biimprd |
|
38 |
|
oveq2 |
|
39 |
38
|
eleq1d |
|
40 |
39
|
biimprd |
|
41 |
37 40
|
jaoa |
|
42 |
34 41
|
mpan9 |
|
43 |
15 42
|
sylan2b |
|
44 |
3 23 33 43
|
iunconn |
|
45 |
13 44
|
eqeltrrd |
|
46 |
45
|
ex |
|
47 |
46
|
3expia |
|
48 |
47
|
exlimdv |
|
49 |
1 48
|
syl5bi |
|
50 |
49
|
3impia |
|