Step |
Hyp |
Ref |
Expression |
1 |
|
elnmz.1 |
|
2 |
|
nmzsubg.2 |
|
3 |
|
nmzsubg.3 |
|
4 |
1
|
ssrab3 |
|
5 |
4
|
a1i |
|
6 |
|
eqid |
|
7 |
2 6
|
grpidcl |
|
8 |
2 3 6
|
grplid |
|
9 |
2 3 6
|
grprid |
|
10 |
8 9
|
eqtr4d |
|
11 |
10
|
eleq1d |
|
12 |
11
|
ralrimiva |
|
13 |
1
|
elnmz |
|
14 |
7 12 13
|
sylanbrc |
|
15 |
14
|
ne0d |
|
16 |
|
id |
|
17 |
4
|
sseli |
|
18 |
4
|
sseli |
|
19 |
2 3
|
grpcl |
|
20 |
16 17 18 19
|
syl3an |
|
21 |
|
simpl1 |
|
22 |
|
simpl2 |
|
23 |
4 22
|
sselid |
|
24 |
|
simpl3 |
|
25 |
4 24
|
sselid |
|
26 |
|
simpr |
|
27 |
2 3
|
grpass |
|
28 |
21 23 25 26 27
|
syl13anc |
|
29 |
28
|
eleq1d |
|
30 |
2 3
|
grpcl |
|
31 |
21 25 26 30
|
syl3anc |
|
32 |
1
|
nmzbi |
|
33 |
22 31 32
|
syl2anc |
|
34 |
2 3
|
grpass |
|
35 |
21 25 26 23 34
|
syl13anc |
|
36 |
35
|
eleq1d |
|
37 |
2 3
|
grpcl |
|
38 |
21 26 23 37
|
syl3anc |
|
39 |
1
|
nmzbi |
|
40 |
24 38 39
|
syl2anc |
|
41 |
33 36 40
|
3bitrd |
|
42 |
2 3
|
grpass |
|
43 |
21 26 23 25 42
|
syl13anc |
|
44 |
43
|
eleq1d |
|
45 |
29 41 44
|
3bitrd |
|
46 |
45
|
ralrimiva |
|
47 |
1
|
elnmz |
|
48 |
20 46 47
|
sylanbrc |
|
49 |
48
|
3expa |
|
50 |
49
|
ralrimiva |
|
51 |
|
eqid |
|
52 |
2 51
|
grpinvcl |
|
53 |
17 52
|
sylan2 |
|
54 |
|
simplr |
|
55 |
|
simpll |
|
56 |
53
|
adantr |
|
57 |
|
simpr |
|
58 |
2 3
|
grpcl |
|
59 |
55 57 56 58
|
syl3anc |
|
60 |
2 3
|
grpcl |
|
61 |
55 56 59 60
|
syl3anc |
|
62 |
1
|
nmzbi |
|
63 |
54 61 62
|
syl2anc |
|
64 |
4 54
|
sselid |
|
65 |
2 3 6 51
|
grprinv |
|
66 |
55 64 65
|
syl2anc |
|
67 |
66
|
oveq1d |
|
68 |
2 3
|
grpass |
|
69 |
55 64 56 59 68
|
syl13anc |
|
70 |
2 3 6
|
grplid |
|
71 |
55 59 70
|
syl2anc |
|
72 |
67 69 71
|
3eqtr3d |
|
73 |
72
|
eleq1d |
|
74 |
2 3
|
grpass |
|
75 |
55 56 59 64 74
|
syl13anc |
|
76 |
2 3
|
grpass |
|
77 |
55 57 56 64 76
|
syl13anc |
|
78 |
2 3 6 51
|
grplinv |
|
79 |
55 64 78
|
syl2anc |
|
80 |
79
|
oveq2d |
|
81 |
2 3 6
|
grprid |
|
82 |
55 57 81
|
syl2anc |
|
83 |
77 80 82
|
3eqtrd |
|
84 |
83
|
oveq2d |
|
85 |
75 84
|
eqtrd |
|
86 |
85
|
eleq1d |
|
87 |
63 73 86
|
3bitr3rd |
|
88 |
87
|
ralrimiva |
|
89 |
1
|
elnmz |
|
90 |
53 88 89
|
sylanbrc |
|
91 |
50 90
|
jca |
|
92 |
91
|
ralrimiva |
|
93 |
2 3 51
|
issubg2 |
|
94 |
5 15 92 93
|
mpbir3and |
|