Step |
Hyp |
Ref |
Expression |
1 |
|
noetasuplem.1 |
|
2 |
|
noetasuplem.2 |
|
3 |
|
simpl1 |
|
4 |
|
simpl2 |
|
5 |
|
simpr |
|
6 |
1
|
nosupbnd1 |
|
7 |
3 4 5 6
|
syl3anc |
|
8 |
2
|
reseq1i |
|
9 |
|
resundir |
|
10 |
|
df-res |
|
11 |
|
incom |
|
12 |
|
disjdif |
|
13 |
11 12
|
eqtri |
|
14 |
|
xpdisj1 |
|
15 |
13 14
|
ax-mp |
|
16 |
10 15
|
eqtri |
|
17 |
16
|
uneq2i |
|
18 |
|
un0 |
|
19 |
9 17 18
|
3eqtri |
|
20 |
8 19
|
eqtri |
|
21 |
1
|
nosupno |
|
22 |
3 4 21
|
syl2anc |
|
23 |
|
nofun |
|
24 |
22 23
|
syl |
|
25 |
|
funrel |
|
26 |
|
resdm |
|
27 |
24 25 26
|
3syl |
|
28 |
20 27
|
syl5eq |
|
29 |
7 28
|
breqtrrd |
|
30 |
|
simp1 |
|
31 |
30
|
sselda |
|
32 |
1 2
|
noetasuplem1 |
|
33 |
32
|
adantr |
|
34 |
|
nodmon |
|
35 |
22 34
|
syl |
|
36 |
|
sltres |
|
37 |
31 33 35 36
|
syl3anc |
|
38 |
29 37
|
mpd |
|