Step |
Hyp |
Ref |
Expression |
1 |
|
subrgascl.p |
|
2 |
|
subrgascl.a |
|
3 |
|
subrgascl.h |
|
4 |
|
subrgascl.u |
|
5 |
|
subrgascl.i |
|
6 |
|
subrgascl.r |
|
7 |
|
subrgasclcl.b |
|
8 |
|
subrgasclcl.k |
|
9 |
|
subrgasclcl.x |
|
10 |
|
iftrue |
|
11 |
10
|
eleq1d |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
|
eqid |
|
17 |
|
subrgrcl |
|
18 |
6 17
|
syl |
|
19 |
1 14 16 8 2 5 18 9
|
mplascl |
|
20 |
19
|
adantr |
|
21 |
3
|
subrgring |
|
22 |
6 21
|
syl |
|
23 |
12 4 7 5 22
|
mplsubrg |
|
24 |
15
|
subrgss |
|
25 |
23 24
|
syl |
|
26 |
25
|
sselda |
|
27 |
20 26
|
eqeltrrd |
|
28 |
12 13 14 15 27
|
psrelbas |
|
29 |
|
eqid |
|
30 |
29
|
fmpt |
|
31 |
28 30
|
sylibr |
|
32 |
5
|
adantr |
|
33 |
14
|
psrbag0 |
|
34 |
32 33
|
syl |
|
35 |
11 31 34
|
rspcdva |
|
36 |
3
|
subrgbas |
|
37 |
6 36
|
syl |
|
38 |
37
|
adantr |
|
39 |
35 38
|
eleqtrrd |
|
40 |
|
eqid |
|
41 |
1 2 3 4 5 6 40
|
subrgascl |
|
42 |
41
|
fveq1d |
|
43 |
|
fvres |
|
44 |
42 43
|
sylan9eq |
|
45 |
|
eqid |
|
46 |
4
|
mplring |
|
47 |
4
|
mpllmod |
|
48 |
|
eqid |
|
49 |
40 45 46 47 48 7
|
asclf |
|
50 |
5 22 49
|
syl2anc |
|
51 |
50
|
adantr |
|
52 |
4 5 22
|
mplsca |
|
53 |
52
|
fveq2d |
|
54 |
37 53
|
eqtrd |
|
55 |
54
|
eleq2d |
|
56 |
55
|
biimpa |
|
57 |
51 56
|
ffvelrnd |
|
58 |
44 57
|
eqeltrrd |
|
59 |
39 58
|
impbida |
|