Step |
Hyp |
Ref |
Expression |
1 |
|
h1datom.1 |
|
2 |
|
h1datom.2 |
|
3 |
1
|
chne0i |
|
4 |
|
ssel |
|
5 |
2
|
h1de2ci |
|
6 |
|
oveq1 |
|
7 |
|
ax-hvmul0 |
|
8 |
2 7
|
ax-mp |
|
9 |
6 8
|
eqtrdi |
|
10 |
|
eqeq1 |
|
11 |
9 10
|
syl5ibr |
|
12 |
11
|
necon3d |
|
13 |
12
|
adantl |
|
14 |
|
reccl |
|
15 |
1
|
chshii |
|
16 |
|
shmulcl |
|
17 |
15 16
|
mp3an1 |
|
18 |
17
|
ex |
|
19 |
14 18
|
syl |
|
20 |
19
|
adantr |
|
21 |
|
oveq2 |
|
22 |
|
simpl |
|
23 |
|
ax-hvmulass |
|
24 |
2 23
|
mp3an3 |
|
25 |
14 22 24
|
syl2anc |
|
26 |
|
recid2 |
|
27 |
26
|
oveq1d |
|
28 |
25 27
|
eqtr3d |
|
29 |
|
ax-hvmulid |
|
30 |
2 29
|
ax-mp |
|
31 |
28 30
|
eqtrdi |
|
32 |
21 31
|
sylan9eqr |
|
33 |
32
|
eleq1d |
|
34 |
20 33
|
sylibd |
|
35 |
34
|
exp31 |
|
36 |
35
|
com23 |
|
37 |
36
|
imp |
|
38 |
13 37
|
syld |
|
39 |
38
|
com3r |
|
40 |
39
|
expd |
|
41 |
40
|
rexlimdv |
|
42 |
5 41
|
syl5bi |
|
43 |
4 42
|
sylcom |
|
44 |
43
|
rexlimdv |
|
45 |
3 44
|
syl5bi |
|
46 |
|
snssi |
|
47 |
|
snssi |
|
48 |
2 47
|
ax-mp |
|
49 |
1
|
chssii |
|
50 |
48 49
|
occon2i |
|
51 |
46 50
|
syl |
|
52 |
1
|
ococi |
|
53 |
51 52
|
sseqtrdi |
|
54 |
45 53
|
syl6 |
|
55 |
54
|
anc2li |
|
56 |
|
eqss |
|
57 |
55 56
|
syl6ibr |
|
58 |
57
|
necon1d |
|
59 |
|
neor |
|
60 |
58 59
|
sylibr |
|