Step |
Hyp |
Ref |
Expression |
1 |
|
emcl.1 |
|
2 |
|
emcl.2 |
|
3 |
|
emcl.3 |
|
4 |
|
emcl.4 |
|
5 |
|
nnuz |
|
6 |
|
1zzd |
|
7 |
1 2 3 4
|
emcllem6 |
|
8 |
7
|
simpri |
|
9 |
8
|
a1i |
|
10 |
1 2
|
emcllem1 |
|
11 |
10
|
simpri |
|
12 |
11
|
ffvelrni |
|
13 |
12
|
adantl |
|
14 |
5 6 9 13
|
climrecl |
|
15 |
|
1nn |
|
16 |
|
simpr |
|
17 |
8
|
a1i |
|
18 |
12
|
adantl |
|
19 |
1 2
|
emcllem2 |
|
20 |
19
|
simprd |
|
21 |
20
|
adantl |
|
22 |
5 16 17 18 21
|
climub |
|
23 |
22
|
ralrimiva |
|
24 |
|
fveq2 |
|
25 |
|
oveq2 |
|
26 |
25
|
sumeq1d |
|
27 |
|
1z |
|
28 |
|
ax-1cn |
|
29 |
|
oveq2 |
|
30 |
|
1div1e1 |
|
31 |
29 30
|
eqtrdi |
|
32 |
31
|
fsum1 |
|
33 |
27 28 32
|
mp2an |
|
34 |
26 33
|
eqtrdi |
|
35 |
|
oveq1 |
|
36 |
|
df-2 |
|
37 |
35 36
|
eqtr4di |
|
38 |
37
|
fveq2d |
|
39 |
34 38
|
oveq12d |
|
40 |
|
1re |
|
41 |
|
2rp |
|
42 |
|
relogcl |
|
43 |
41 42
|
ax-mp |
|
44 |
40 43
|
resubcli |
|
45 |
44
|
elexi |
|
46 |
39 2 45
|
fvmpt |
|
47 |
15 46
|
ax-mp |
|
48 |
24 47
|
eqtrdi |
|
49 |
48
|
breq1d |
|
50 |
49
|
rspcva |
|
51 |
15 23 50
|
sylancr |
|
52 |
|
fveq2 |
|
53 |
52
|
negeqd |
|
54 |
|
eqid |
|
55 |
|
negex |
|
56 |
53 54 55
|
fvmpt |
|
57 |
56
|
adantl |
|
58 |
7
|
simpli |
|
59 |
58
|
a1i |
|
60 |
|
0cnd |
|
61 |
|
nnex |
|
62 |
61
|
mptex |
|
63 |
62
|
a1i |
|
64 |
10
|
simpli |
|
65 |
64
|
ffvelrni |
|
66 |
65
|
adantl |
|
67 |
66
|
recnd |
|
68 |
|
fveq2 |
|
69 |
68
|
negeqd |
|
70 |
|
negex |
|
71 |
69 54 70
|
fvmpt |
|
72 |
71
|
adantl |
|
73 |
|
df-neg |
|
74 |
72 73
|
eqtrdi |
|
75 |
5 6 59 60 63 67 74
|
climsubc2 |
|
76 |
75
|
adantr |
|
77 |
66
|
renegcld |
|
78 |
72 77
|
eqeltrd |
|
79 |
78
|
adantlr |
|
80 |
19
|
simpld |
|
81 |
80
|
adantl |
|
82 |
|
peano2nn |
|
83 |
82
|
adantl |
|
84 |
64
|
ffvelrni |
|
85 |
83 84
|
syl |
|
86 |
85 66
|
lenegd |
|
87 |
81 86
|
mpbid |
|
88 |
|
fveq2 |
|
89 |
88
|
negeqd |
|
90 |
|
negex |
|
91 |
89 54 90
|
fvmpt |
|
92 |
83 91
|
syl |
|
93 |
87 72 92
|
3brtr4d |
|
94 |
93
|
adantlr |
|
95 |
5 16 76 79 94
|
climub |
|
96 |
57 95
|
eqbrtrrd |
|
97 |
|
df-neg |
|
98 |
96 97
|
breqtrrdi |
|
99 |
14
|
mptru |
|
100 |
64
|
ffvelrni |
|
101 |
100
|
adantl |
|
102 |
|
leneg |
|
103 |
99 101 102
|
sylancr |
|
104 |
98 103
|
mpbird |
|
105 |
104
|
ralrimiva |
|
106 |
|
fveq2 |
|
107 |
|
fveq2 |
|
108 |
|
log1 |
|
109 |
107 108
|
eqtrdi |
|
110 |
34 109
|
oveq12d |
|
111 |
|
1m0e1 |
|
112 |
110 111
|
eqtrdi |
|
113 |
40
|
elexi |
|
114 |
112 1 113
|
fvmpt |
|
115 |
15 114
|
ax-mp |
|
116 |
106 115
|
eqtrdi |
|
117 |
116
|
breq2d |
|
118 |
117
|
rspcva |
|
119 |
15 105 118
|
sylancr |
|
120 |
44 40
|
elicc2i |
|
121 |
14 51 119 120
|
syl3anbrc |
|
122 |
|
ffn |
|
123 |
64 122
|
mp1i |
|
124 |
16 5
|
eleqtrdi |
|
125 |
|
elfznn |
|
126 |
125
|
adantl |
|
127 |
126 65
|
syl |
|
128 |
|
elfznn |
|
129 |
128
|
adantl |
|
130 |
129 80
|
syl |
|
131 |
124 127 130
|
monoord2 |
|
132 |
131 115
|
breqtrdi |
|
133 |
99 40
|
elicc2i |
|
134 |
101 104 132 133
|
syl3anbrc |
|
135 |
134
|
ralrimiva |
|
136 |
|
ffnfv |
|
137 |
123 135 136
|
sylanbrc |
|
138 |
|
ffn |
|
139 |
11 138
|
mp1i |
|
140 |
11
|
ffvelrni |
|
141 |
140
|
adantl |
|
142 |
126 12
|
syl |
|
143 |
129 20
|
syl |
|
144 |
124 142 143
|
monoord |
|
145 |
47 144
|
eqbrtrrid |
|
146 |
44 99
|
elicc2i |
|
147 |
141 145 22 146
|
syl3anbrc |
|
148 |
147
|
ralrimiva |
|
149 |
|
ffnfv |
|
150 |
139 148 149
|
sylanbrc |
|
151 |
121 137 150
|
3jca |
|
152 |
151
|
mptru |
|