Step |
Hyp |
Ref |
Expression |
1 |
|
metakunt12.1 |
|
2 |
|
metakunt12.2 |
|
3 |
|
metakunt12.3 |
|
4 |
|
metakunt12.4 |
|
5 |
|
metakunt12.5 |
|
6 |
|
metakunt12.6 |
|
7 |
|
ioran |
|
8 |
4
|
a1i |
|
9 |
|
eqeq1 |
|
10 |
|
breq1 |
|
11 |
|
id |
|
12 |
|
oveq1 |
|
13 |
10 11 12
|
ifbieq12d |
|
14 |
9 13
|
ifbieq2d |
|
15 |
14
|
adantl |
|
16 |
5
|
a1i |
|
17 |
|
eqeq1 |
|
18 |
|
breq1 |
|
19 |
|
id |
|
20 |
|
oveq1 |
|
21 |
18 19 20
|
ifbieq12d |
|
22 |
17 21
|
ifbieq2d |
|
23 |
22
|
adantl |
|
24 |
|
simp2 |
|
25 |
|
iffalse |
|
26 |
24 25
|
syl |
|
27 |
|
simp3 |
|
28 |
|
iffalse |
|
29 |
27 28
|
syl |
|
30 |
26 29
|
eqtrd |
|
31 |
30
|
adantr |
|
32 |
23 31
|
eqtrd |
|
33 |
6
|
3ad2ant1 |
|
34 |
6
|
elfzelzd |
|
35 |
34
|
3ad2ant1 |
|
36 |
35
|
peano2zd |
|
37 |
16 32 33 36
|
fvmptd |
|
38 |
|
eqeq1 |
|
39 |
|
breq1 |
|
40 |
|
id |
|
41 |
|
oveq1 |
|
42 |
39 40 41
|
ifbieq12d |
|
43 |
38 42
|
ifbieq2d |
|
44 |
37 43
|
syl |
|
45 |
2
|
nnred |
|
46 |
45
|
3ad2ant1 |
|
47 |
35
|
zred |
|
48 |
36
|
zred |
|
49 |
46 47
|
lenltd |
|
50 |
27 49
|
mpbird |
|
51 |
47
|
ltp1d |
|
52 |
46 47 48 50 51
|
lelttrd |
|
53 |
46 52
|
ltned |
|
54 |
53
|
necomd |
|
55 |
54
|
neneqd |
|
56 |
|
iffalse |
|
57 |
55 56
|
syl |
|
58 |
47
|
lep1d |
|
59 |
46 47 48 50 58
|
letrd |
|
60 |
46 48
|
lenltd |
|
61 |
59 60
|
mpbid |
|
62 |
|
iffalse |
|
63 |
61 62
|
syl |
|
64 |
35
|
zcnd |
|
65 |
|
1cnd |
|
66 |
64 65
|
pncand |
|
67 |
57 63 66
|
3eqtrd |
|
68 |
44 67
|
eqtrd |
|
69 |
68
|
adantr |
|
70 |
15 69
|
eqtrd |
|
71 |
1 2 3 5
|
metakunt2 |
|
72 |
71
|
3ad2ant1 |
|
73 |
72 33
|
ffvelrnd |
|
74 |
8 70 73 33
|
fvmptd |
|
75 |
74
|
3expb |
|
76 |
7 75
|
sylan2b |
|