Step |
Hyp |
Ref |
Expression |
1 |
|
subrgply1.s |
|
2 |
|
subrgply1.h |
|
3 |
|
subrgply1.u |
|
4 |
|
subrgply1.b |
|
5 |
|
gsumply1subr.s |
|
6 |
|
gsumply1subr.a |
|
7 |
|
gsumply1subr.f |
|
8 |
1 2 3 4
|
subrgply1 |
|
9 |
|
subrgsubg |
|
10 |
|
subgsubm |
|
11 |
9 10
|
syl |
|
12 |
5 8 11
|
3syl |
|
13 |
|
eqid |
|
14 |
6 12 7 13
|
gsumsubm |
|
15 |
7 6
|
fexd |
|
16 |
|
ovexd |
|
17 |
3
|
fvexi |
|
18 |
17
|
a1i |
|
19 |
|
eqid |
|
20 |
4
|
oveq2i |
|
21 |
1 2 3 19 5 20
|
ressply1bas |
|
22 |
21
|
eqcomd |
|
23 |
13
|
subrgring |
|
24 |
8 23
|
syl |
|
25 |
|
ringmgm |
|
26 |
5 24 25
|
3syl |
|
27 |
|
simpl |
|
28 |
1 2 3 4 5 13
|
ressply1bas |
|
29 |
28
|
eqcomd |
|
30 |
29
|
eleq2d |
|
31 |
30
|
biimpcd |
|
32 |
31
|
adantr |
|
33 |
32
|
impcom |
|
34 |
29
|
eleq2d |
|
35 |
34
|
biimpcd |
|
36 |
35
|
adantl |
|
37 |
36
|
impcom |
|
38 |
1 2 3 4 5 13
|
ressply1add |
|
39 |
27 33 37 38
|
syl12anc |
|
40 |
39
|
eqcomd |
|
41 |
7
|
ffund |
|
42 |
7
|
frnd |
|
43 |
42 28
|
sseqtrd |
|
44 |
15 16 18 22 26 40 41 43
|
gsummgmpropd |
|
45 |
14 44
|
eqtrd |
|