Step |
Hyp |
Ref |
Expression |
1 |
|
mpomulcn.j |
|
2 |
|
divcn.k |
|
3 |
|
df-div |
|
4 |
|
eldifsn |
|
5 |
|
divval |
|
6 |
|
divrec |
|
7 |
5 6
|
eqtr3d |
|
8 |
7
|
3expb |
|
9 |
4 8
|
sylan2b |
|
10 |
9
|
mpoeq3ia |
|
11 |
3 10
|
eqtri |
|
12 |
1
|
cnfldtopon |
|
13 |
12
|
a1i |
|
14 |
|
difss |
|
15 |
|
resttopon |
|
16 |
13 14 15
|
sylancl |
|
17 |
2 16
|
eqeltrid |
|
18 |
13 17
|
cnmpt1st |
|
19 |
13 17
|
cnmpt2nd |
|
20 |
|
eqid |
|
21 |
|
eldifi |
|
22 |
|
eldifsni |
|
23 |
21 22
|
reccld |
|
24 |
20 23
|
fmpti |
|
25 |
|
eqid |
|
26 |
25
|
reccn2 |
|
27 |
|
ovres |
|
28 |
|
eldifi |
|
29 |
|
eldifi |
|
30 |
|
eqid |
|
31 |
30
|
cnmetdval |
|
32 |
|
abssub |
|
33 |
31 32
|
eqtrd |
|
34 |
28 29 33
|
syl2an |
|
35 |
27 34
|
eqtrd |
|
36 |
35
|
breq1d |
|
37 |
|
oveq2 |
|
38 |
|
ovex |
|
39 |
37 20 38
|
fvmpt |
|
40 |
|
oveq2 |
|
41 |
|
ovex |
|
42 |
40 20 41
|
fvmpt |
|
43 |
39 42
|
oveqan12d |
|
44 |
|
eldifsni |
|
45 |
28 44
|
reccld |
|
46 |
|
eldifsni |
|
47 |
29 46
|
reccld |
|
48 |
30
|
cnmetdval |
|
49 |
|
abssub |
|
50 |
48 49
|
eqtrd |
|
51 |
45 47 50
|
syl2an |
|
52 |
43 51
|
eqtrd |
|
53 |
52
|
breq1d |
|
54 |
36 53
|
imbi12d |
|
55 |
54
|
ralbidva |
|
56 |
55
|
rexbidv |
|
57 |
56
|
adantr |
|
58 |
26 57
|
mpbird |
|
59 |
58
|
rgen2 |
|
60 |
|
cnxmet |
|
61 |
|
xmetres2 |
|
62 |
60 14 61
|
mp2an |
|
63 |
|
eqid |
|
64 |
1
|
cnfldtopn |
|
65 |
|
eqid |
|
66 |
63 64 65
|
metrest |
|
67 |
60 14 66
|
mp2an |
|
68 |
2 67
|
eqtri |
|
69 |
68 64
|
metcn |
|
70 |
62 60 69
|
mp2an |
|
71 |
24 59 70
|
mpbir2an |
|
72 |
71
|
a1i |
|
73 |
13 17 19 17 72 40
|
cnmpt21 |
|
74 |
1
|
mpomulcn |
|
75 |
74
|
a1i |
|
76 |
|
oveq12 |
|
77 |
13 17 18 73 13 13 75 76
|
cnmpt22 |
|
78 |
77
|
mptru |
|
79 |
11 78
|
eqeltri |
|