Step |
Hyp |
Ref |
Expression |
1 |
|
archiabllem.b |
|
2 |
|
archiabllem.0 |
|
3 |
|
archiabllem.e |
|
4 |
|
archiabllem.t |
|
5 |
|
archiabllem.m |
|
6 |
|
archiabllem.g |
|
7 |
|
archiabllem.a |
|
8 |
|
archiabllem2.1 |
|
9 |
|
archiabllem2.2 |
|
10 |
|
archiabllem2.3 |
|
11 |
|
archiabllem2a.4 |
|
12 |
|
archiabllem2a.5 |
|
13 |
|
simpllr |
|
14 |
|
simplrl |
|
15 |
|
simpr |
|
16 |
|
breq2 |
|
17 |
|
id |
|
18 |
17 17
|
oveq12d |
|
19 |
18
|
breq1d |
|
20 |
16 19
|
anbi12d |
|
21 |
20
|
rspcev |
|
22 |
13 14 15 21
|
syl12anc |
|
23 |
|
simplll |
|
24 |
|
ogrpgrp |
|
25 |
23 6 24
|
3syl |
|
26 |
23 11
|
syl |
|
27 |
|
simpllr |
|
28 |
|
eqid |
|
29 |
1 28
|
grpsubcl |
|
30 |
25 26 27 29
|
syl3anc |
|
31 |
1 2 28
|
grpsubid |
|
32 |
25 27 31
|
syl2anc |
|
33 |
23 6
|
syl |
|
34 |
|
simplrr |
|
35 |
1 4 28
|
ogrpsublt |
|
36 |
33 27 26 27 34 35
|
syl131anc |
|
37 |
32 36
|
eqbrtrrd |
|
38 |
23 9
|
syl |
|
39 |
1 8
|
grpcl |
|
40 |
25 27 27 39
|
syl3anc |
|
41 |
|
simpr |
|
42 |
1 4 28
|
ogrpsublt |
|
43 |
33 26 40 27 41 42
|
syl131anc |
|
44 |
1 8 28
|
grpaddsubass |
|
45 |
25 27 27 27 44
|
syl13anc |
|
46 |
32
|
oveq2d |
|
47 |
1 8 2
|
grprid |
|
48 |
25 27 47
|
syl2anc |
|
49 |
45 46 48
|
3eqtrd |
|
50 |
43 49
|
breqtrd |
|
51 |
1 4 8 25 38 30 27 30 50
|
ogrpaddltrd |
|
52 |
1 8 28
|
grpnpcan |
|
53 |
25 26 27 52
|
syl3anc |
|
54 |
51 53
|
breqtrd |
|
55 |
|
ovexd |
|
56 |
3 4
|
pltle |
|
57 |
25 55 26 56
|
syl3anc |
|
58 |
54 57
|
mpd |
|
59 |
|
breq2 |
|
60 |
|
id |
|
61 |
60 60
|
oveq12d |
|
62 |
61
|
breq1d |
|
63 |
59 62
|
anbi12d |
|
64 |
63
|
rspcev |
|
65 |
30 37 58 64
|
syl12anc |
|
66 |
6
|
ad2antrr |
|
67 |
|
isogrp |
|
68 |
67
|
simprbi |
|
69 |
|
omndtos |
|
70 |
66 68 69
|
3syl |
|
71 |
66 24
|
syl |
|
72 |
|
simplr |
|
73 |
71 72 72 39
|
syl3anc |
|
74 |
11
|
ad2antrr |
|
75 |
1 3 4
|
tlt2 |
|
76 |
70 73 74 75
|
syl3anc |
|
77 |
22 65 76
|
mpjaodan |
|
78 |
10
|
3expia |
|
79 |
78
|
ralrimiva |
|
80 |
|
breq2 |
|
81 |
|
breq2 |
|
82 |
81
|
anbi2d |
|
83 |
82
|
rexbidv |
|
84 |
80 83
|
imbi12d |
|
85 |
84
|
rspcv |
|
86 |
11 79 12 85
|
syl3c |
|
87 |
77 86
|
r19.29a |
|