Step |
Hyp |
Ref |
Expression |
1 |
|
sge0pr.a |
|
2 |
|
sge0pr.b |
|
3 |
|
sge0pr.d |
|
4 |
|
sge0pr.e |
|
5 |
|
sge0pr.cd |
|
6 |
|
sge0pr.ce |
|
7 |
|
sge0pr.ab |
|
8 |
|
iccssxr |
|
9 |
8 4
|
sseldi |
|
10 |
|
mnfxr |
|
11 |
10
|
a1i |
|
12 |
|
0xr |
|
13 |
12
|
a1i |
|
14 |
|
mnflt0 |
|
15 |
14
|
a1i |
|
16 |
|
pnfxr |
|
17 |
16
|
a1i |
|
18 |
|
iccgelb |
|
19 |
13 17 4 18
|
syl3anc |
|
20 |
11 13 9 15 19
|
xrltletrd |
|
21 |
11 9 20
|
xrgtned |
|
22 |
|
xaddpnf2 |
|
23 |
9 21 22
|
syl2anc |
|
24 |
23
|
eqcomd |
|
25 |
24
|
adantr |
|
26 |
|
prex |
|
27 |
26
|
a1i |
|
28 |
5
|
adantl |
|
29 |
3
|
adantr |
|
30 |
28 29
|
eqeltrd |
|
31 |
30
|
adantlr |
|
32 |
|
simpll |
|
33 |
|
simpl |
|
34 |
|
neqne |
|
35 |
34
|
adantl |
|
36 |
|
elprn1 |
|
37 |
33 35 36
|
syl2anc |
|
38 |
37
|
adantll |
|
39 |
6
|
adantl |
|
40 |
4
|
adantr |
|
41 |
39 40
|
eqeltrd |
|
42 |
32 38 41
|
syl2anc |
|
43 |
31 42
|
pm2.61dan |
|
44 |
|
eqid |
|
45 |
43 44
|
fmptd |
|
46 |
45
|
adantr |
|
47 |
|
id |
|
48 |
47
|
eqcomd |
|
49 |
48
|
adantl |
|
50 |
|
prid1g |
|
51 |
3 50
|
syl |
|
52 |
1 2 44 5 6
|
rnmptpr |
|
53 |
52
|
eqcomd |
|
54 |
51 53
|
eleqtrd |
|
55 |
54
|
adantr |
|
56 |
49 55
|
eqeltrd |
|
57 |
27 46 56
|
sge0pnfval |
|
58 |
|
oveq1 |
|
59 |
58
|
adantl |
|
60 |
25 57 59
|
3eqtr4d |
|
61 |
8 3
|
sseldi |
|
62 |
|
iccgelb |
|
63 |
13 17 3 62
|
syl3anc |
|
64 |
11 13 61 15 63
|
xrltletrd |
|
65 |
11 61 64
|
xrgtned |
|
66 |
|
xaddpnf1 |
|
67 |
61 65 66
|
syl2anc |
|
68 |
67
|
eqcomd |
|
69 |
68
|
adantr |
|
70 |
26
|
a1i |
|
71 |
45
|
adantr |
|
72 |
|
id |
|
73 |
72
|
eqcomd |
|
74 |
73
|
adantl |
|
75 |
|
prid2g |
|
76 |
4 75
|
syl |
|
77 |
76 53
|
eleqtrd |
|
78 |
77
|
adantr |
|
79 |
74 78
|
eqeltrd |
|
80 |
70 71 79
|
sge0pnfval |
|
81 |
|
oveq2 |
|
82 |
81
|
adantl |
|
83 |
69 80 82
|
3eqtr4d |
|
84 |
83
|
adantlr |
|
85 |
|
rge0ssre |
|
86 |
|
ax-resscn |
|
87 |
85 86
|
sstri |
|
88 |
12
|
a1i |
|
89 |
16
|
a1i |
|
90 |
61
|
adantr |
|
91 |
63
|
adantr |
|
92 |
|
pnfge |
|
93 |
61 92
|
syl |
|
94 |
93
|
adantr |
|
95 |
47
|
necon3bi |
|
96 |
95
|
adantl |
|
97 |
90 89 94 96
|
xrleneltd |
|
98 |
88 89 90 91 97
|
elicod |
|
99 |
98
|
adantr |
|
100 |
87 99
|
sseldi |
|
101 |
12
|
a1i |
|
102 |
16
|
a1i |
|
103 |
9
|
adantr |
|
104 |
19
|
adantr |
|
105 |
|
pnfge |
|
106 |
9 105
|
syl |
|
107 |
106
|
adantr |
|
108 |
72
|
necon3bi |
|
109 |
108
|
adantl |
|
110 |
103 102 107 109
|
xrleneltd |
|
111 |
101 102 103 104 110
|
elicod |
|
112 |
87 111
|
sseldi |
|
113 |
112
|
adantlr |
|
114 |
100 113
|
jca |
|
115 |
1 2
|
jca |
|
116 |
115
|
ad2antrr |
|
117 |
7
|
ad2antrr |
|
118 |
5 6 114 116 117
|
sumpr |
|
119 |
|
prfi |
|
120 |
119
|
a1i |
|
121 |
5
|
adantl |
|
122 |
98
|
adantr |
|
123 |
121 122
|
eqeltrd |
|
124 |
123
|
ad4ant14 |
|
125 |
|
simp-4l |
|
126 |
|
simpllr |
|
127 |
37
|
adantll |
|
128 |
39
|
3adant2 |
|
129 |
111
|
3adant3 |
|
130 |
128 129
|
eqeltrd |
|
131 |
125 126 127 130
|
syl3anc |
|
132 |
124 131
|
pm2.61dan |
|
133 |
120 132
|
sge0fsummpt |
|
134 |
85 99
|
sseldi |
|
135 |
85 111
|
sseldi |
|
136 |
135
|
adantlr |
|
137 |
|
rexadd |
|
138 |
134 136 137
|
syl2anc |
|
139 |
118 133 138
|
3eqtr4d |
|
140 |
84 139
|
pm2.61dan |
|
141 |
60 140
|
pm2.61dan |
|