Step |
Hyp |
Ref |
Expression |
1 |
|
sge0sn.1 |
|
2 |
|
sge0sn.2 |
|
3 |
|
snex |
|
4 |
3
|
a1i |
|
5 |
2
|
adantr |
|
6 |
|
id |
|
7 |
6
|
eqcomd |
|
8 |
7
|
adantl |
|
9 |
2
|
ffund |
|
10 |
9
|
adantr |
|
11 |
|
snidg |
|
12 |
1 11
|
syl |
|
13 |
2
|
fdmd |
|
14 |
13
|
eqcomd |
|
15 |
12 14
|
eleqtrd |
|
16 |
15
|
adantr |
|
17 |
|
fvelrn |
|
18 |
10 16 17
|
syl2anc |
|
19 |
8 18
|
eqeltrd |
|
20 |
4 5 19
|
sge0pnfval |
|
21 |
|
simpr |
|
22 |
20 21
|
eqtr4d |
|
23 |
3
|
a1i |
|
24 |
2
|
adantr |
|
25 |
|
elsni |
|
26 |
25
|
eqcomd |
|
27 |
26
|
con3i |
|
28 |
27
|
adantl |
|
29 |
1 2
|
rnsnf |
|
30 |
29
|
eqcomd |
|
31 |
30
|
adantr |
|
32 |
28 31
|
neleqtrd |
|
33 |
24 32
|
fge0iccico |
|
34 |
23 33
|
sge0reval |
|
35 |
|
sum0 |
|
36 |
35
|
eqcomi |
|
37 |
36
|
a1i |
|
38 |
|
nfcvd |
|
39 |
|
nfv |
|
40 |
|
fveq2 |
|
41 |
40
|
adantl |
|
42 |
1
|
adantr |
|
43 |
|
rge0ssre |
|
44 |
|
ax-resscn |
|
45 |
43 44
|
sstri |
|
46 |
42 11
|
syl |
|
47 |
33 46
|
ffvelrnd |
|
48 |
45 47
|
sseldi |
|
49 |
38 39 41 42 48
|
sumsnd |
|
50 |
49
|
eqcomd |
|
51 |
37 50
|
preq12d |
|
52 |
51
|
supeq1d |
|
53 |
|
xrltso |
|
54 |
53
|
a1i |
|
55 |
|
0xr |
|
56 |
55
|
a1i |
|
57 |
|
iccssxr |
|
58 |
2 12
|
ffvelrnd |
|
59 |
57 58
|
sseldi |
|
60 |
|
suppr |
|
61 |
54 56 59 60
|
syl3anc |
|
62 |
|
pnfxr |
|
63 |
62
|
a1i |
|
64 |
56 63 58
|
3jca |
|
65 |
|
iccgelb |
|
66 |
64 65
|
syl |
|
67 |
56 59
|
xrlenltd |
|
68 |
66 67
|
mpbid |
|
69 |
68
|
iffalsed |
|
70 |
61 69
|
eqtr2d |
|
71 |
70
|
adantr |
|
72 |
|
pwsn |
|
73 |
72
|
ineq1i |
|
74 |
|
0fin |
|
75 |
|
snfi |
|
76 |
|
prssi |
|
77 |
74 75 76
|
mp2an |
|
78 |
|
df-ss |
|
79 |
78
|
biimpi |
|
80 |
77 79
|
ax-mp |
|
81 |
73 80
|
eqtri |
|
82 |
|
mpteq1 |
|
83 |
81 82
|
ax-mp |
|
84 |
|
0ex |
|
85 |
84
|
a1i |
|
86 |
3
|
a1i |
|
87 |
|
sumex |
|
88 |
87
|
a1i |
|
89 |
|
sumex |
|
90 |
89
|
a1i |
|
91 |
|
sumeq1 |
|
92 |
91
|
adantl |
|
93 |
|
sumeq1 |
|
94 |
93
|
adantl |
|
95 |
85 86 88 90 92 94
|
fmptpr |
|
96 |
95
|
mptru |
|
97 |
96
|
eqcomi |
|
98 |
83 97
|
eqtri |
|
99 |
98
|
rneqi |
|
100 |
|
rnpropg |
|
101 |
84 3 100
|
mp2an |
|
102 |
99 101
|
eqtri |
|
103 |
102
|
supeq1i |
|
104 |
103
|
a1i |
|
105 |
52 71 104
|
3eqtr4d |
|
106 |
34 105
|
eqtr4d |
|
107 |
22 106
|
pm2.61dan |
|