Step |
Hyp |
Ref |
Expression |
1 |
|
ngpgrp |
|
2 |
1
|
adantr |
|
3 |
|
ngpms |
|
4 |
3
|
adantr |
|
5 |
|
mstps |
|
6 |
4 5
|
syl |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
7 8
|
grpsubf |
|
10 |
2 9
|
syl |
|
11 |
|
rphalfcl |
|
12 |
|
simplll |
|
13 |
12 4
|
syl |
|
14 |
|
simpllr |
|
15 |
14
|
simpld |
|
16 |
|
simprl |
|
17 |
|
eqid |
|
18 |
7 17
|
mscl |
|
19 |
13 15 16 18
|
syl3anc |
|
20 |
14
|
simprd |
|
21 |
|
simprr |
|
22 |
7 17
|
mscl |
|
23 |
13 20 21 22
|
syl3anc |
|
24 |
|
rpre |
|
25 |
24
|
ad2antlr |
|
26 |
|
lt2halves |
|
27 |
19 23 25 26
|
syl3anc |
|
28 |
12 2
|
syl |
|
29 |
7 8
|
grpsubcl |
|
30 |
28 15 20 29
|
syl3anc |
|
31 |
7 8
|
grpsubcl |
|
32 |
28 16 21 31
|
syl3anc |
|
33 |
7 8
|
grpsubcl |
|
34 |
28 16 20 33
|
syl3anc |
|
35 |
7 17
|
mstri |
|
36 |
13 30 32 34 35
|
syl13anc |
|
37 |
12
|
simpld |
|
38 |
7 8 17
|
ngpsubcan |
|
39 |
37 15 16 20 38
|
syl13anc |
|
40 |
|
eqid |
|
41 |
|
eqid |
|
42 |
7 40 41 8
|
grpsubval |
|
43 |
16 20 42
|
syl2anc |
|
44 |
7 40 41 8
|
grpsubval |
|
45 |
44
|
adantl |
|
46 |
43 45
|
oveq12d |
|
47 |
7 41
|
grpinvcl |
|
48 |
28 20 47
|
syl2anc |
|
49 |
7 41
|
grpinvcl |
|
50 |
28 21 49
|
syl2anc |
|
51 |
7 40 17
|
ngplcan |
|
52 |
12 48 50 16 51
|
syl13anc |
|
53 |
7 41 17
|
ngpinvds |
|
54 |
12 20 21 53
|
syl12anc |
|
55 |
46 52 54
|
3eqtrd |
|
56 |
39 55
|
oveq12d |
|
57 |
36 56
|
breqtrd |
|
58 |
7 17
|
mscl |
|
59 |
13 30 32 58
|
syl3anc |
|
60 |
19 23
|
readdcld |
|
61 |
|
lelttr |
|
62 |
59 60 25 61
|
syl3anc |
|
63 |
57 62
|
mpand |
|
64 |
27 63
|
syld |
|
65 |
15 16
|
ovresd |
|
66 |
65
|
breq1d |
|
67 |
20 21
|
ovresd |
|
68 |
67
|
breq1d |
|
69 |
66 68
|
anbi12d |
|
70 |
30 32
|
ovresd |
|
71 |
70
|
breq1d |
|
72 |
64 69 71
|
3imtr4d |
|
73 |
72
|
ralrimivva |
|
74 |
|
breq2 |
|
75 |
|
breq2 |
|
76 |
74 75
|
anbi12d |
|
77 |
76
|
imbi1d |
|
78 |
77
|
2ralbidv |
|
79 |
78
|
rspcev |
|
80 |
11 73 79
|
syl2an2 |
|
81 |
80
|
ralrimiva |
|
82 |
81
|
ralrimivva |
|
83 |
|
msxms |
|
84 |
|
eqid |
|
85 |
7 84
|
xmsxmet |
|
86 |
4 83 85
|
3syl |
|
87 |
|
eqid |
|
88 |
87 87 87
|
txmetcn |
|
89 |
86 86 86 88
|
syl3anc |
|
90 |
10 82 89
|
mpbir2and |
|
91 |
|
eqid |
|
92 |
91 7 84
|
mstopn |
|
93 |
4 92
|
syl |
|
94 |
93 93
|
oveq12d |
|
95 |
94 93
|
oveq12d |
|
96 |
90 95
|
eleqtrrd |
|
97 |
91 8
|
istgp2 |
|
98 |
2 6 96 97
|
syl3anbrc |
|