Step |
Hyp |
Ref |
Expression |
1 |
|
dvmptfprodlem.xph |
|
2 |
|
dvmptfprodlem.iph |
|
3 |
|
dvmptfprodlem.jph |
|
4 |
|
dvmptfprodlem.if |
|
5 |
|
dvmptfprodlem.jg |
|
6 |
|
dvmptfprodlem.a |
|
7 |
|
dvmptfprodlem.d |
|
8 |
|
dvmptfprodlem.e |
|
9 |
|
dvmptfprodlem.db |
|
10 |
|
dvmptfprodlem.ss |
|
11 |
|
dvmptfprodlem.s |
|
12 |
|
dvmptfprodlem.c |
|
13 |
|
dvmptfprodlem.dvp |
|
14 |
|
dvmptfprodlem.14 |
|
15 |
|
dvmptfprodlem.dvf |
|
16 |
|
dvmptfprodlem.f |
|
17 |
|
dvmptfprodlem.cg |
|
18 |
|
nfcv |
|
19 |
|
nfcv |
|
20 |
18 19
|
nfel |
|
21 |
2 20
|
nfan |
|
22 |
4
|
a1i |
|
23 |
|
snfi |
|
24 |
23
|
a1i |
|
25 |
|
unfi |
|
26 |
7 24 25
|
syl2anc |
|
27 |
26
|
adantr |
|
28 |
|
simpll |
|
29 |
10
|
sselda |
|
30 |
29
|
adantlr |
|
31 |
|
simplr |
|
32 |
28 30 31 6
|
syl3anc |
|
33 |
|
snidg |
|
34 |
8 33
|
syl |
|
35 |
|
elun2 |
|
36 |
34 35
|
syl |
|
37 |
36
|
adantr |
|
38 |
16
|
adantl |
|
39 |
21 22 27 32 37 38
|
fprodsplit1f |
|
40 |
|
difundir |
|
41 |
40
|
a1i |
|
42 |
|
difsn |
|
43 |
9 42
|
syl |
|
44 |
|
difid |
|
45 |
44
|
a1i |
|
46 |
43 45
|
uneq12d |
|
47 |
|
un0 |
|
48 |
47
|
a1i |
|
49 |
41 46 48
|
3eqtrd |
|
50 |
49
|
prodeq1d |
|
51 |
50
|
oveq2d |
|
52 |
51
|
adantr |
|
53 |
39 52
|
eqtrd |
|
54 |
1 53
|
mpteq2da |
|
55 |
54
|
oveq2d |
|
56 |
10 36
|
sseldd |
|
57 |
56
|
adantr |
|
58 |
|
simpl |
|
59 |
|
simpr |
|
60 |
58 57 59
|
3jca |
|
61 |
|
nfcv |
|
62 |
|
nfv |
|
63 |
2 62 20
|
nf3an |
|
64 |
|
nfcv |
|
65 |
4 64
|
nfel |
|
66 |
63 65
|
nfim |
|
67 |
|
ancom |
|
68 |
67
|
imbi1i |
|
69 |
|
eqcom |
|
70 |
69
|
imbi2i |
|
71 |
68 70
|
bitri |
|
72 |
38 71
|
mpbi |
|
73 |
72
|
3adantr2 |
|
74 |
73
|
3adant2 |
|
75 |
|
simp3 |
|
76 |
|
eleq1 |
|
77 |
76
|
3anbi2d |
|
78 |
77
|
imbi1d |
|
79 |
78
|
biimpa |
|
80 |
79
|
3adant3 |
|
81 |
75 80
|
mpd |
|
82 |
74 81
|
eqeltrd |
|
83 |
82
|
3exp |
|
84 |
6
|
2a1i |
|
85 |
83 84
|
impbid |
|
86 |
61 66 85 6
|
vtoclgf |
|
87 |
57 60 86
|
sylc |
|
88 |
58 7
|
syl |
|
89 |
58
|
adantr |
|
90 |
10
|
adantr |
|
91 |
|
elun1 |
|
92 |
91
|
adantl |
|
93 |
90 92
|
sseldd |
|
94 |
93
|
adantlr |
|
95 |
59
|
adantr |
|
96 |
89 94 95 6
|
syl3anc |
|
97 |
21 88 96
|
fprodclf |
|
98 |
|
nfv |
|
99 |
3 98
|
nfan |
|
100 |
|
diffi |
|
101 |
7 100
|
syl |
|
102 |
101
|
adantr |
|
103 |
|
eldifi |
|
104 |
103
|
adantl |
|
105 |
104 96
|
syldan |
|
106 |
21 102 105
|
fprodclf |
|
107 |
106
|
adantr |
|
108 |
12 107
|
mulcld |
|
109 |
99 88 108
|
fsumclf |
|
110 |
1 11 87 14 15 97 109 13
|
dvmptmulf |
|
111 |
|
nfcv |
|
112 |
|
nfcv |
|
113 |
5 111 112
|
nfov |
|
114 |
58 8
|
syl |
|
115 |
58 9
|
syl |
|
116 |
|
diffi |
|
117 |
26 116
|
syl |
|
118 |
117
|
adantr |
|
119 |
|
eldifi |
|
120 |
119
|
adantl |
|
121 |
120 32
|
syldan |
|
122 |
21 118 121
|
fprodclf |
|
123 |
122
|
adantr |
|
124 |
12 123
|
mulcld |
|
125 |
|
sneq |
|
126 |
125
|
difeq2d |
|
127 |
126
|
prodeq1d |
|
128 |
17 127
|
oveq12d |
|
129 |
49 7
|
eqeltrd |
|
130 |
129
|
adantr |
|
131 |
58
|
adantr |
|
132 |
10
|
adantr |
|
133 |
|
eldifi |
|
134 |
133
|
adantl |
|
135 |
132 134
|
sseldd |
|
136 |
135
|
adantlr |
|
137 |
59
|
adantr |
|
138 |
131 136 137 6
|
syl3anc |
|
139 |
21 130 138
|
fprodclf |
|
140 |
14 139
|
mulcld |
|
141 |
99 113 88 114 115 124 128 140
|
fsumsplitsn |
|
142 |
|
difundir |
|
143 |
142
|
a1i |
|
144 |
|
nfv |
|
145 |
1 144
|
nfan |
|
146 |
|
elsni |
|
147 |
146
|
eqcomd |
|
148 |
147
|
adantr |
|
149 |
|
simpr |
|
150 |
|
eqidd |
|
151 |
148 149 150
|
3eqtrd |
|
152 |
151
|
adantll |
|
153 |
|
simpllr |
|
154 |
152 153
|
eqeltrd |
|
155 |
9
|
ad3antrrr |
|
156 |
154 155
|
pm2.65da |
|
157 |
|
velsn |
|
158 |
156 157
|
sylnibr |
|
159 |
158
|
ex |
|
160 |
145 159
|
ralrimi |
|
161 |
|
disj |
|
162 |
160 161
|
sylibr |
|
163 |
|
disjdif2 |
|
164 |
162 163
|
syl |
|
165 |
164
|
uneq2d |
|
166 |
143 165
|
eqtrd |
|
167 |
166
|
prodeq1d |
|
168 |
167
|
adantlr |
|
169 |
|
nfv |
|
170 |
21 169
|
nfan |
|
171 |
102
|
adantr |
|
172 |
58
|
adantr |
|
173 |
172 8
|
syl |
|
174 |
|
id |
|
175 |
174
|
intnanrd |
|
176 |
174 175
|
syl |
|
177 |
|
eldif |
|
178 |
176 177
|
sylnibr |
|
179 |
9 178
|
syl |
|
180 |
172 179
|
syl |
|
181 |
105
|
adantlr |
|
182 |
87
|
adantr |
|
183 |
170 4 171 173 180 181 16 182
|
fprodsplitsn |
|
184 |
|
eqidd |
|
185 |
168 183 184
|
3eqtrd |
|
186 |
185
|
oveq2d |
|
187 |
12 107 182
|
mulassd |
|
188 |
187
|
eqcomd |
|
189 |
186 188
|
eqtrd |
|
190 |
189
|
ex |
|
191 |
99 190
|
ralrimi |
|
192 |
191
|
sumeq2d |
|
193 |
99 88 87 108
|
fsummulc1f |
|
194 |
193
|
eqcomd |
|
195 |
|
eqidd |
|
196 |
192 194 195
|
3eqtrd |
|
197 |
109 87
|
mulcld |
|
198 |
196 197
|
eqeltrd |
|
199 |
198 140
|
addcomd |
|
200 |
50
|
oveq2d |
|
201 |
200
|
adantr |
|
202 |
201 196
|
oveq12d |
|
203 |
141 199 202
|
3eqtrrd |
|
204 |
1 203
|
mpteq2da |
|
205 |
55 110 204
|
3eqtrd |
|