Step |
Hyp |
Ref |
Expression |
1 |
|
subrgpsr.s |
|
2 |
|
subrgpsr.h |
|
3 |
|
subrgpsr.u |
|
4 |
|
subrgpsr.b |
|
5 |
|
simpl |
|
6 |
|
subrgrcl |
|
7 |
6
|
adantl |
|
8 |
1 5 7
|
psrring |
|
9 |
2
|
subrgring |
|
10 |
9
|
adantl |
|
11 |
3 5 10
|
psrring |
|
12 |
4
|
a1i |
|
13 |
|
eqid |
|
14 |
|
simpr |
|
15 |
1 2 3 4 13 14
|
resspsrbas |
|
16 |
1 2 3 4 13 14
|
resspsradd |
|
17 |
1 2 3 4 13 14
|
resspsrmul |
|
18 |
12 15 16 17
|
ringpropd |
|
19 |
11 18
|
mpbid |
|
20 |
|
eqid |
|
21 |
13 20
|
ressbasss |
|
22 |
15 21
|
eqsstrdi |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
|
eqid |
|
26 |
|
eqid |
|
27 |
1 5 7 23 24 25 26
|
psr1 |
|
28 |
25
|
subrg1cl |
|
29 |
|
subrgsubg |
|
30 |
24
|
subg0cl |
|
31 |
29 30
|
syl |
|
32 |
28 31
|
ifcld |
|
33 |
32
|
adantl |
|
34 |
2
|
subrgbas |
|
35 |
34
|
adantl |
|
36 |
33 35
|
eleqtrd |
|
37 |
36
|
adantr |
|
38 |
27 37
|
fmpt3d |
|
39 |
|
fvex |
|
40 |
|
ovex |
|
41 |
40
|
rabex |
|
42 |
39 41
|
elmap |
|
43 |
38 42
|
sylibr |
|
44 |
|
eqid |
|
45 |
3 44 23 4 5
|
psrbas |
|
46 |
43 45
|
eleqtrrd |
|
47 |
22 46
|
jca |
|
48 |
20 26
|
issubrg |
|
49 |
8 19 47 48
|
syl21anbrc |
|