Step |
Hyp |
Ref |
Expression |
1 |
|
mulgnndir.b |
|
2 |
|
mulgnndir.t |
|
3 |
|
mulgnndir.p |
|
4 |
|
simpl1 |
|
5 |
|
grpmnd |
|
6 |
4 5
|
syl |
|
7 |
|
simprl |
|
8 |
|
simprr |
|
9 |
|
simpl23 |
|
10 |
1 2 3
|
mulgnn0dir |
|
11 |
6 7 8 9 10
|
syl13anc |
|
12 |
11
|
anassrs |
|
13 |
|
simpl1 |
|
14 |
|
simp22 |
|
15 |
14
|
adantr |
|
16 |
|
simpl23 |
|
17 |
|
eqid |
|
18 |
1 2 17
|
mulgneg |
|
19 |
13 15 16 18
|
syl3anc |
|
20 |
19
|
oveq1d |
|
21 |
1 2
|
mulgcl |
|
22 |
13 15 16 21
|
syl3anc |
|
23 |
|
eqid |
|
24 |
1 3 23 17
|
grplinv |
|
25 |
13 22 24
|
syl2anc |
|
26 |
20 25
|
eqtrd |
|
27 |
26
|
oveq2d |
|
28 |
|
simpl3 |
|
29 |
|
nn0z |
|
30 |
28 29
|
syl |
|
31 |
1 2
|
mulgcl |
|
32 |
13 30 16 31
|
syl3anc |
|
33 |
1 3 23
|
grprid |
|
34 |
13 32 33
|
syl2anc |
|
35 |
27 34
|
eqtrd |
|
36 |
|
nn0z |
|
37 |
36
|
ad2antll |
|
38 |
1 2
|
mulgcl |
|
39 |
13 37 16 38
|
syl3anc |
|
40 |
1 3
|
grpass |
|
41 |
13 32 39 22 40
|
syl13anc |
|
42 |
13 5
|
syl |
|
43 |
|
simprr |
|
44 |
1 2 3
|
mulgnn0dir |
|
45 |
42 28 43 16 44
|
syl13anc |
|
46 |
|
simp21 |
|
47 |
46
|
zcnd |
|
48 |
14
|
zcnd |
|
49 |
47 48
|
addcld |
|
50 |
49
|
adantr |
|
51 |
48
|
adantr |
|
52 |
50 51
|
negsubd |
|
53 |
47
|
adantr |
|
54 |
53 51
|
pncand |
|
55 |
52 54
|
eqtrd |
|
56 |
55
|
oveq1d |
|
57 |
45 56
|
eqtr3d |
|
58 |
57
|
oveq1d |
|
59 |
41 58
|
eqtr3d |
|
60 |
35 59
|
eqtr3d |
|
61 |
60
|
anassrs |
|
62 |
|
elznn0 |
|
63 |
62
|
simprbi |
|
64 |
14 63
|
syl |
|
65 |
64
|
adantr |
|
66 |
12 61 65
|
mpjaodan |
|
67 |
|
simpl1 |
|
68 |
46
|
adantr |
|
69 |
|
simpl23 |
|
70 |
1 2
|
mulgcl |
|
71 |
67 68 69 70
|
syl3anc |
|
72 |
68
|
znegcld |
|
73 |
1 2
|
mulgcl |
|
74 |
67 72 69 73
|
syl3anc |
|
75 |
29
|
3ad2ant3 |
|
76 |
75
|
adantr |
|
77 |
67 76 69 31
|
syl3anc |
|
78 |
1 3
|
grpass |
|
79 |
67 71 74 77 78
|
syl13anc |
|
80 |
1 2 17
|
mulgneg |
|
81 |
67 68 69 80
|
syl3anc |
|
82 |
81
|
oveq2d |
|
83 |
1 3 23 17
|
grprinv |
|
84 |
67 71 83
|
syl2anc |
|
85 |
82 84
|
eqtrd |
|
86 |
85
|
oveq1d |
|
87 |
1 3 23
|
grplid |
|
88 |
67 77 87
|
syl2anc |
|
89 |
86 88
|
eqtrd |
|
90 |
67 5
|
syl |
|
91 |
|
simpr |
|
92 |
|
simpl3 |
|
93 |
1 2 3
|
mulgnn0dir |
|
94 |
90 91 92 69 93
|
syl13anc |
|
95 |
47
|
adantr |
|
96 |
95
|
negcld |
|
97 |
49
|
adantr |
|
98 |
96 97
|
addcomd |
|
99 |
97 95
|
negsubd |
|
100 |
48
|
adantr |
|
101 |
95 100
|
pncan2d |
|
102 |
98 99 101
|
3eqtrd |
|
103 |
102
|
oveq1d |
|
104 |
94 103
|
eqtr3d |
|
105 |
104
|
oveq2d |
|
106 |
79 89 105
|
3eqtr3d |
|
107 |
|
elznn0 |
|
108 |
107
|
simprbi |
|
109 |
46 108
|
syl |
|
110 |
66 106 109
|
mpjaodan |
|