Step |
Hyp |
Ref |
Expression |
1 |
|
etransclem32.s |
|
2 |
|
etransclem32.x |
|
3 |
|
etransclem32.p |
|
4 |
|
etransclem32.m |
|
5 |
|
etransclem32.f |
|
6 |
|
etransclem32.n |
|
7 |
|
etransclem32.ngt |
|
8 |
|
etransclem32.h |
|
9 |
|
etransclem11 |
|
10 |
1 2 3 4 5 6 8 9
|
etransclem30 |
|
11 |
|
simpr |
|
12 |
9 6
|
etransclem12 |
|
13 |
12
|
adantr |
|
14 |
11 13
|
eleqtrd |
|
15 |
14
|
adantlr |
|
16 |
|
nfv |
|
17 |
|
nfre1 |
|
18 |
17
|
nfn |
|
19 |
16 18
|
nfan |
|
20 |
|
fzssre |
|
21 |
|
rabid |
|
22 |
21
|
simplbi |
|
23 |
|
elmapi |
|
24 |
22 23
|
syl |
|
25 |
24
|
adantl |
|
26 |
25
|
ffvelrnda |
|
27 |
20 26
|
sseldi |
|
28 |
27
|
adantlr |
|
29 |
|
nnm1nn0 |
|
30 |
3 29
|
syl |
|
31 |
30
|
nn0red |
|
32 |
3
|
nnred |
|
33 |
31 32
|
ifcld |
|
34 |
33
|
ad3antrrr |
|
35 |
|
ralnex |
|
36 |
35
|
biimpri |
|
37 |
36
|
r19.21bi |
|
38 |
37
|
adantll |
|
39 |
28 34 38
|
nltled |
|
40 |
39
|
ex |
|
41 |
19 40
|
ralrimi |
|
42 |
|
fveq2 |
|
43 |
42
|
cbvsumv |
|
44 |
21
|
simprbi |
|
45 |
43 44
|
syl5reqr |
|
46 |
45
|
ad2antlr |
|
47 |
|
fveq2 |
|
48 |
47
|
cbvsumv |
|
49 |
|
fzfid |
|
50 |
25
|
ffvelrnda |
|
51 |
20 50
|
sseldi |
|
52 |
51
|
adantlr |
|
53 |
31 32
|
ifcld |
|
54 |
53
|
ad3antrrr |
|
55 |
|
eqeq1 |
|
56 |
55
|
ifbid |
|
57 |
47 56
|
breq12d |
|
58 |
57
|
rspccva |
|
59 |
58
|
adantll |
|
60 |
49 52 54 59
|
fsumle |
|
61 |
|
nn0uz |
|
62 |
4 61
|
eleqtrdi |
|
63 |
3
|
nnnn0d |
|
64 |
30 63
|
ifcld |
|
65 |
64
|
adantr |
|
66 |
65
|
nn0cnd |
|
67 |
|
iftrue |
|
68 |
62 66 67
|
fsum1p |
|
69 |
|
0p1e1 |
|
70 |
69
|
oveq1i |
|
71 |
70
|
a1i |
|
72 |
71
|
sumeq1d |
|
73 |
|
0red |
|
74 |
|
1red |
|
75 |
|
elfzelz |
|
76 |
75
|
zred |
|
77 |
|
0lt1 |
|
78 |
77
|
a1i |
|
79 |
|
elfzle1 |
|
80 |
73 74 76 78 79
|
ltletrd |
|
81 |
80
|
gt0ne0d |
|
82 |
81
|
neneqd |
|
83 |
82
|
iffalsed |
|
84 |
83
|
adantl |
|
85 |
84
|
sumeq2dv |
|
86 |
|
fzfid |
|
87 |
3
|
nncnd |
|
88 |
|
fsumconst |
|
89 |
86 87 88
|
syl2anc |
|
90 |
|
hashfz1 |
|
91 |
4 90
|
syl |
|
92 |
91
|
oveq1d |
|
93 |
89 92
|
eqtrd |
|
94 |
72 85 93
|
3eqtrd |
|
95 |
94
|
oveq2d |
|
96 |
30
|
nn0cnd |
|
97 |
4 63
|
nn0mulcld |
|
98 |
97
|
nn0cnd |
|
99 |
96 98
|
addcomd |
|
100 |
68 95 99
|
3eqtrd |
|
101 |
100
|
ad2antrr |
|
102 |
60 101
|
breqtrd |
|
103 |
48 102
|
eqbrtrid |
|
104 |
46 103
|
eqbrtrd |
|
105 |
41 104
|
syldan |
|
106 |
97 30
|
nn0addcld |
|
107 |
106
|
nn0red |
|
108 |
6
|
nn0red |
|
109 |
107 108
|
ltnled |
|
110 |
7 109
|
mpbid |
|
111 |
110
|
ad2antrr |
|
112 |
105 111
|
condan |
|
113 |
112
|
adantlr |
|
114 |
|
nfv |
|
115 |
|
nfcv |
|
116 |
115
|
nfsum1 |
|
117 |
116
|
nfeq1 |
|
118 |
|
nfcv |
|
119 |
117 118
|
nfrabw |
|
120 |
119
|
nfcri |
|
121 |
114 120
|
nfan |
|
122 |
|
nfv |
|
123 |
|
nfv |
|
124 |
121 122 123
|
nf3an |
|
125 |
|
nfcv |
|
126 |
|
fzfid |
|
127 |
1
|
ad3antrrr |
|
128 |
2
|
ad3antrrr |
|
129 |
3
|
ad3antrrr |
|
130 |
|
etransclem5 |
|
131 |
8 130
|
eqtri |
|
132 |
|
simpr |
|
133 |
24
|
ad2antlr |
|
134 |
|
simpr |
|
135 |
133 134
|
ffvelrnd |
|
136 |
135
|
adantllr |
|
137 |
|
elfznn0 |
|
138 |
136 137
|
syl |
|
139 |
127 128 129 131 132 138
|
etransclem20 |
|
140 |
|
simpllr |
|
141 |
139 140
|
ffvelrnd |
|
142 |
141
|
3ad2antl1 |
|
143 |
|
fveq2 |
|
144 |
143
|
oveq2d |
|
145 |
144 42
|
fveq12d |
|
146 |
145
|
fveq1d |
|
147 |
|
simp2 |
|
148 |
1
|
ad2antrr |
|
149 |
148
|
3ad2ant1 |
|
150 |
2
|
ad2antrr |
|
151 |
150
|
3ad2ant1 |
|
152 |
3
|
ad2antrr |
|
153 |
152
|
3ad2ant1 |
|
154 |
|
etransclem5 |
|
155 |
8 154
|
eqtri |
|
156 |
|
fzssz |
|
157 |
156 26
|
sseldi |
|
158 |
157
|
adantllr |
|
159 |
158
|
3adant3 |
|
160 |
|
simp3 |
|
161 |
149 151 153 155 147 159 160
|
etransclem19 |
|
162 |
|
eqidd |
|
163 |
|
simp1lr |
|
164 |
|
0red |
|
165 |
161 162 163 164
|
fvmptd |
|
166 |
124 125 126 142 146 147 165
|
fprod0 |
|
167 |
166
|
rexlimdv3a |
|
168 |
113 167
|
mpd |
|
169 |
15 168
|
syldan |
|
170 |
169
|
oveq2d |
|
171 |
6
|
faccld |
|
172 |
171
|
nncnd |
|
173 |
172
|
adantr |
|
174 |
|
fzfid |
|
175 |
|
simpll |
|
176 |
14
|
adantr |
|
177 |
|
simpr |
|
178 |
175 176 177 135
|
syl21anc |
|
179 |
178 137
|
syl |
|
180 |
179
|
faccld |
|
181 |
180
|
nncnd |
|
182 |
174 181
|
fprodcl |
|
183 |
180
|
nnne0d |
|
184 |
174 181 183
|
fprodn0 |
|
185 |
173 182 184
|
divcld |
|
186 |
185
|
mul01d |
|
187 |
186
|
adantlr |
|
188 |
170 187
|
eqtrd |
|
189 |
188
|
sumeq2dv |
|
190 |
|
eqid |
|
191 |
190 6
|
etransclem16 |
|
192 |
191
|
olcd |
|
193 |
192
|
adantr |
|
194 |
|
sumz |
|
195 |
193 194
|
syl |
|
196 |
189 195
|
eqtrd |
|
197 |
196
|
mpteq2dva |
|
198 |
10 197
|
eqtrd |
|