Step |
Hyp |
Ref |
Expression |
1 |
|
nsmallnq |
|
2 |
|
abn0 |
|
3 |
1 2
|
sylibr |
|
4 |
|
0pss |
|
5 |
3 4
|
sylibr |
|
6 |
|
ltrelnq |
|
7 |
6
|
brel |
|
8 |
7
|
simpld |
|
9 |
8
|
abssi |
|
10 |
|
ltsonq |
|
11 |
10 6
|
soirri |
|
12 |
|
breq1 |
|
13 |
12
|
elabg |
|
14 |
11 13
|
mtbiri |
|
15 |
14
|
ancli |
|
16 |
|
ssnelpss |
|
17 |
9 15 16
|
mpsyl |
|
18 |
|
vex |
|
19 |
|
breq1 |
|
20 |
18 19
|
elab |
|
21 |
10 6
|
sotri |
|
22 |
21
|
expcom |
|
23 |
22
|
adantl |
|
24 |
|
vex |
|
25 |
|
breq1 |
|
26 |
24 25
|
elab |
|
27 |
23 26
|
syl6ibr |
|
28 |
27
|
alrimiv |
|
29 |
|
ltbtwnnq |
|
30 |
26
|
anbi2i |
|
31 |
30
|
biimpri |
|
32 |
31
|
ancomd |
|
33 |
32
|
eximi |
|
34 |
29 33
|
sylbi |
|
35 |
34
|
adantl |
|
36 |
|
df-rex |
|
37 |
35 36
|
sylibr |
|
38 |
28 37
|
jca |
|
39 |
20 38
|
sylan2b |
|
40 |
39
|
ralrimiva |
|
41 |
|
elnp |
|
42 |
5 17 40 41
|
syl21anbrc |
|