Step |
Hyp |
Ref |
Expression |
1 |
|
tngngp.t |
|
2 |
|
tngngp.x |
|
3 |
|
tngngp.m |
|
4 |
|
tngngp.z |
|
5 |
|
eqid |
|
6 |
1 2 5
|
tngngp2 |
|
7 |
6
|
simprbda |
|
8 |
|
simplr |
|
9 |
|
simpr |
|
10 |
2
|
fvexi |
|
11 |
|
reex |
|
12 |
|
fex2 |
|
13 |
10 11 12
|
mp3an23 |
|
14 |
13
|
ad2antrr |
|
15 |
1 2
|
tngbas |
|
16 |
14 15
|
syl |
|
17 |
9 16
|
eleqtrd |
|
18 |
|
eqid |
|
19 |
|
eqid |
|
20 |
|
eqid |
|
21 |
18 19 20
|
nmeq0 |
|
22 |
8 17 21
|
syl2anc |
|
23 |
7
|
adantr |
|
24 |
|
simpll |
|
25 |
1 2 11
|
tngnm |
|
26 |
23 24 25
|
syl2anc |
|
27 |
26
|
fveq1d |
|
28 |
27
|
eqeq1d |
|
29 |
1 4
|
tng0 |
|
30 |
14 29
|
syl |
|
31 |
30
|
eqeq2d |
|
32 |
22 28 31
|
3bitr4d |
|
33 |
|
simpllr |
|
34 |
17
|
adantr |
|
35 |
16
|
eleq2d |
|
36 |
35
|
biimpa |
|
37 |
|
eqid |
|
38 |
18 19 37
|
nmmtri |
|
39 |
33 34 36 38
|
syl3anc |
|
40 |
2 16
|
syl5eqr |
|
41 |
|
eqid |
|
42 |
1 41
|
tngplusg |
|
43 |
14 42
|
syl |
|
44 |
40 43
|
grpsubpropd |
|
45 |
3 44
|
syl5eq |
|
46 |
45
|
oveqd |
|
47 |
26 46
|
fveq12d |
|
48 |
47
|
adantr |
|
49 |
26
|
fveq1d |
|
50 |
27 49
|
oveq12d |
|
51 |
50
|
adantr |
|
52 |
39 48 51
|
3brtr4d |
|
53 |
52
|
ralrimiva |
|
54 |
32 53
|
jca |
|
55 |
54
|
ralrimiva |
|
56 |
7 55
|
jca |
|
57 |
|
simprl |
|
58 |
|
simpl |
|
59 |
|
simpl |
|
60 |
59
|
ralimi |
|
61 |
60
|
ad2antll |
|
62 |
|
fveq2 |
|
63 |
62
|
eqeq1d |
|
64 |
|
eqeq1 |
|
65 |
63 64
|
bibi12d |
|
66 |
65
|
rspccva |
|
67 |
61 66
|
sylan |
|
68 |
|
simpr |
|
69 |
68
|
ralimi |
|
70 |
69
|
ad2antll |
|
71 |
|
fvoveq1 |
|
72 |
62
|
oveq1d |
|
73 |
71 72
|
breq12d |
|
74 |
|
oveq2 |
|
75 |
74
|
fveq2d |
|
76 |
|
fveq2 |
|
77 |
76
|
oveq2d |
|
78 |
75 77
|
breq12d |
|
79 |
73 78
|
rspc2va |
|
80 |
79
|
ancoms |
|
81 |
70 80
|
sylan |
|
82 |
1 2 3 4 57 58 67 81
|
tngngpd |
|
83 |
56 82
|
impbida |
|