Step |
Hyp |
Ref |
Expression |
1 |
|
metakunt30.1 |
|
2 |
|
metakunt30.2 |
|
3 |
|
metakunt30.3 |
|
4 |
|
metakunt30.4 |
|
5 |
|
metakunt30.5 |
|
6 |
|
metakunt30.6 |
|
7 |
|
metakunt30.7 |
|
8 |
|
metakunt30.8 |
|
9 |
|
metakunt30.9 |
|
10 |
|
metakunt30.10 |
|
11 |
1 2 3 4 5 6 7 8
|
metakunt28 |
|
12 |
11
|
fveq2d |
|
13 |
9
|
a1i |
|
14 |
|
elfznn |
|
15 |
4 14
|
syl |
|
16 |
|
nnre |
|
17 |
15 16
|
syl |
|
18 |
2
|
nnred |
|
19 |
17 18
|
resubcld |
|
20 |
1
|
nnred |
|
21 |
20 18
|
resubcld |
|
22 |
|
elfzle2 |
|
23 |
4 22
|
syl |
|
24 |
17 20 18 23
|
lesub1dd |
|
25 |
2
|
nnrpd |
|
26 |
20 25
|
ltsubrpd |
|
27 |
19 21 20 24 26
|
lelttrd |
|
28 |
19 27
|
ltned |
|
29 |
28
|
adantr |
|
30 |
|
neeq1 |
|
31 |
30
|
adantl |
|
32 |
29 31
|
mpbird |
|
33 |
32
|
neneqd |
|
34 |
33
|
iffalsed |
|
35 |
18 19
|
lenltd |
|
36 |
35
|
biimpa |
|
37 |
36
|
3adant2 |
|
38 |
|
breq1 |
|
39 |
38
|
3ad2ant2 |
|
40 |
37 39
|
mtbird |
|
41 |
40
|
iffalsed |
|
42 |
|
simp2 |
|
43 |
42
|
oveq1d |
|
44 |
|
simp3 |
|
45 |
44
|
iftrued |
|
46 |
45
|
eqcomd |
|
47 |
10
|
a1i |
|
48 |
47
|
eqcomd |
|
49 |
46 48
|
eqtrd |
|
50 |
49
|
oveq2d |
|
51 |
43 50
|
eqtrd |
|
52 |
41 51
|
eqtrd |
|
53 |
52
|
3expa |
|
54 |
|
simpr |
|
55 |
19
|
adantr |
|
56 |
18
|
adantr |
|
57 |
55 56
|
ltnled |
|
58 |
54 57
|
mpbird |
|
59 |
58
|
3adant2 |
|
60 |
38
|
3ad2ant2 |
|
61 |
59 60
|
mpbird |
|
62 |
61
|
iftrued |
|
63 |
|
simp2 |
|
64 |
|
nncn |
|
65 |
15 64
|
syl |
|
66 |
65
|
3ad2ant1 |
|
67 |
2
|
nncnd |
|
68 |
67
|
3ad2ant1 |
|
69 |
66 68
|
subcld |
|
70 |
69
|
addid1d |
|
71 |
70
|
eqcomd |
|
72 |
10
|
a1i |
|
73 |
|
simp3 |
|
74 |
73
|
iffalsed |
|
75 |
72 74
|
eqtrd |
|
76 |
75
|
eqcomd |
|
77 |
76
|
oveq2d |
|
78 |
71 77
|
eqtrd |
|
79 |
63 78
|
eqtrd |
|
80 |
62 79
|
eqtrd |
|
81 |
80
|
3expa |
|
82 |
53 81
|
pm2.61dan |
|
83 |
34 82
|
eqtrd |
|
84 |
|
1zzd |
|
85 |
1
|
nnzd |
|
86 |
15
|
nnzd |
|
87 |
2
|
nnzd |
|
88 |
86 87
|
zsubcld |
|
89 |
|
1m1e0 |
|
90 |
18 17 8
|
nltled |
|
91 |
7
|
neqned |
|
92 |
90 91
|
jca |
|
93 |
18 17
|
ltlend |
|
94 |
92 93
|
mpbird |
|
95 |
18 17
|
posdifd |
|
96 |
94 95
|
mpbid |
|
97 |
89 96
|
eqbrtrid |
|
98 |
|
zlem1lt |
|
99 |
84 88 98
|
syl2anc |
|
100 |
97 99
|
mpbird |
|
101 |
19 20 27
|
ltled |
|
102 |
84 85 88 100 101
|
elfzd |
|
103 |
|
0zd |
|
104 |
84 103
|
ifcld |
|
105 |
10
|
a1i |
|
106 |
105
|
eleq1d |
|
107 |
104 106
|
mpbird |
|
108 |
88 107
|
zaddcld |
|
109 |
13 83 102 108
|
fvmptd |
|
110 |
12 109
|
eqtrd |
|