Step |
Hyp |
Ref |
Expression |
1 |
|
knoppndvlem20.c |
|
2 |
|
knoppndvlem20.n |
|
3 |
|
knoppndvlem20.1 |
|
4 |
1 2 3
|
knoppndvlem12 |
|
5 |
4
|
simprd |
|
6 |
|
2re |
|
7 |
6
|
a1i |
|
8 |
2
|
nnred |
|
9 |
7 8
|
remulcld |
|
10 |
1
|
knoppndvlem3 |
|
11 |
10
|
simpld |
|
12 |
11
|
recnd |
|
13 |
12
|
abscld |
|
14 |
9 13
|
remulcld |
|
15 |
|
1red |
|
16 |
14 15
|
resubcld |
|
17 |
|
0red |
|
18 |
|
0lt1 |
|
19 |
18
|
a1i |
|
20 |
17 15 16 19 5
|
lttrd |
|
21 |
16 20
|
elrpd |
|
22 |
21
|
recgt1d |
|
23 |
5 22
|
mpbid |
|
24 |
21
|
rprecred |
|
25 |
24 15
|
jca |
|
26 |
|
difrp |
|
27 |
25 26
|
syl |
|
28 |
23 27
|
mpbid |
|