Step |
Hyp |
Ref |
Expression |
1 |
|
finodsubmsubg.o |
|
2 |
|
finodsubmsubg.g |
|
3 |
|
finodsubmsubg.s |
|
4 |
|
finodsubmsubg.1 |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
2
|
adantr |
|
9 |
5
|
submss |
|
10 |
3 9
|
syl |
|
11 |
10
|
sselda |
|
12 |
5 1 6 7 8 11
|
odm1inv |
|
13 |
12
|
adantr |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
|
eqid |
|
17 |
16
|
submmnd |
|
18 |
3 17
|
syl |
|
19 |
18
|
ad2antrr |
|
20 |
|
nnm1nn0 |
|
21 |
20
|
adantl |
|
22 |
|
simplr |
|
23 |
16 5
|
ressbas2 |
|
24 |
10 23
|
syl |
|
25 |
24
|
ad2antrr |
|
26 |
22 25
|
eleqtrd |
|
27 |
14 15 19 21 26
|
mulgnn0cld |
|
28 |
3
|
ad2antrr |
|
29 |
6 16 15
|
submmulg |
|
30 |
28 21 22 29
|
syl3anc |
|
31 |
27 30 25
|
3eltr4d |
|
32 |
13 31
|
eqeltrrd |
|
33 |
32
|
ex |
|
34 |
33
|
ralimdva |
|
35 |
4 34
|
mpd |
|
36 |
7
|
issubg3 |
|
37 |
2 36
|
syl |
|
38 |
3 35 37
|
mpbir2and |
|