Step |
Hyp |
Ref |
Expression |
1 |
|
idlinsubrg.s |
|
2 |
|
idlinsubrg.u |
|
3 |
|
idlinsubrg.v |
|
4 |
|
inss2 |
|
5 |
1
|
subrgbas |
|
6 |
4 5
|
sseqtrid |
|
7 |
6
|
adantr |
|
8 |
|
subrgrcl |
|
9 |
|
eqid |
|
10 |
2 9
|
lidl0cl |
|
11 |
8 10
|
sylan |
|
12 |
|
subrgsubg |
|
13 |
|
subgsubm |
|
14 |
9
|
subm0cl |
|
15 |
12 13 14
|
3syl |
|
16 |
15
|
adantr |
|
17 |
11 16
|
elind |
|
18 |
17
|
ne0d |
|
19 |
|
eqid |
|
20 |
1 19
|
ressplusg |
|
21 |
|
eqid |
|
22 |
1 21
|
ressmulr |
|
23 |
22
|
oveqd |
|
24 |
|
eqidd |
|
25 |
20 23 24
|
oveq123d |
|
26 |
25
|
ad4antr |
|
27 |
8
|
ad4antr |
|
28 |
|
simp-4r |
|
29 |
|
eqid |
|
30 |
29
|
subrgss |
|
31 |
5 30
|
eqsstrrd |
|
32 |
31
|
adantr |
|
33 |
32
|
sselda |
|
34 |
33
|
ad2antrr |
|
35 |
|
inss1 |
|
36 |
35
|
a1i |
|
37 |
36
|
sselda |
|
38 |
37
|
adantr |
|
39 |
2 29 21
|
lidlmcl |
|
40 |
27 28 34 38 39
|
syl22anc |
|
41 |
35
|
a1i |
|
42 |
41
|
sselda |
|
43 |
2 19
|
lidlacl |
|
44 |
27 28 40 42 43
|
syl22anc |
|
45 |
|
simp-4l |
|
46 |
|
simpr |
|
47 |
5
|
ad2antrr |
|
48 |
46 47
|
eleqtrrd |
|
49 |
48
|
ad2antrr |
|
50 |
4
|
a1i |
|
51 |
50
|
sselda |
|
52 |
51
|
adantr |
|
53 |
21
|
subrgmcl |
|
54 |
45 49 52 53
|
syl3anc |
|
55 |
4
|
a1i |
|
56 |
55
|
sselda |
|
57 |
19
|
subrgacl |
|
58 |
45 54 56 57
|
syl3anc |
|
59 |
44 58
|
elind |
|
60 |
26 59
|
eqeltrrd |
|
61 |
60
|
anasss |
|
62 |
61
|
ralrimivva |
|
63 |
62
|
ralrimiva |
|
64 |
|
eqid |
|
65 |
|
eqid |
|
66 |
|
eqid |
|
67 |
3 64 65 66
|
islidl |
|
68 |
7 18 63 67
|
syl3anbrc |
|