Step |
Hyp |
Ref |
Expression |
1 |
|
ocval |
|
2 |
|
ssrab2 |
|
3 |
1 2
|
eqsstrdi |
|
4 |
|
ssel |
|
5 |
|
hi01 |
|
6 |
4 5
|
syl6 |
|
7 |
6
|
ralrimiv |
|
8 |
|
ax-hv0cl |
|
9 |
7 8
|
jctil |
|
10 |
|
ocel |
|
11 |
9 10
|
mpbird |
|
12 |
3 11
|
jca |
|
13 |
|
ssel2 |
|
14 |
|
ax-his2 |
|
15 |
14
|
3expa |
|
16 |
|
oveq12 |
|
17 |
|
00id |
|
18 |
16 17
|
eqtrdi |
|
19 |
15 18
|
sylan9eq |
|
20 |
19
|
ex |
|
21 |
20
|
ancoms |
|
22 |
13 21
|
sylan |
|
23 |
22
|
an32s |
|
24 |
23
|
ralimdva |
|
25 |
24
|
imdistanda |
|
26 |
|
hvaddcl |
|
27 |
26
|
anim1i |
|
28 |
25 27
|
syl6 |
|
29 |
|
ocel |
|
30 |
|
ocel |
|
31 |
29 30
|
anbi12d |
|
32 |
|
an4 |
|
33 |
|
r19.26 |
|
34 |
33
|
anbi2i |
|
35 |
32 34
|
bitr4i |
|
36 |
31 35
|
syl6bb |
|
37 |
|
ocel |
|
38 |
28 36 37
|
3imtr4d |
|
39 |
38
|
ralrimivv |
|
40 |
|
mul01 |
|
41 |
|
oveq2 |
|
42 |
41
|
eqeq1d |
|
43 |
40 42
|
syl5ibrcom |
|
44 |
43
|
ad2antrl |
|
45 |
|
ax-his3 |
|
46 |
45
|
eqeq1d |
|
47 |
46
|
3expa |
|
48 |
47
|
ancoms |
|
49 |
44 48
|
sylibrd |
|
50 |
13 49
|
sylan |
|
51 |
50
|
an32s |
|
52 |
51
|
ralimdva |
|
53 |
52
|
imdistanda |
|
54 |
|
hvmulcl |
|
55 |
54
|
anim1i |
|
56 |
53 55
|
syl6 |
|
57 |
30
|
anbi2d |
|
58 |
|
anass |
|
59 |
57 58
|
bitr4di |
|
60 |
|
ocel |
|
61 |
56 59 60
|
3imtr4d |
|
62 |
61
|
ralrimivv |
|
63 |
39 62
|
jca |
|
64 |
|
issh2 |
|
65 |
12 63 64
|
sylanbrc |
|