| Step |
Hyp |
Ref |
Expression |
| 1 |
|
dvmptfprod.iph |
|
| 2 |
|
dvmptfprod.jph |
|
| 3 |
|
dvmptfprod.j |
|
| 4 |
|
dvmptfprod.k |
|
| 5 |
|
dvmptfprod.s |
|
| 6 |
|
dvmptfprod.x |
|
| 7 |
|
dvmptfprod.i |
|
| 8 |
|
dvmptfprod.a |
|
| 9 |
|
dvmptfprod.b |
|
| 10 |
|
dvmptfprod.d |
|
| 11 |
|
dvmptfprod.bc |
|
| 12 |
|
ssid |
|
| 13 |
12
|
jctr |
|
| 14 |
|
sseq1 |
|
| 15 |
14
|
anbi2d |
|
| 16 |
|
prodeq1 |
|
| 17 |
16
|
mpteq2dv |
|
| 18 |
17
|
oveq2d |
|
| 19 |
|
sumeq1 |
|
| 20 |
|
difeq1 |
|
| 21 |
20
|
prodeq1d |
|
| 22 |
21
|
oveq2d |
|
| 23 |
22
|
sumeq2sdv |
|
| 24 |
19 23
|
eqtrd |
|
| 25 |
24
|
mpteq2dv |
|
| 26 |
18 25
|
eqeq12d |
|
| 27 |
15 26
|
imbi12d |
|
| 28 |
|
sseq1 |
|
| 29 |
28
|
anbi2d |
|
| 30 |
|
prodeq1 |
|
| 31 |
30
|
mpteq2dv |
|
| 32 |
31
|
oveq2d |
|
| 33 |
|
sumeq1 |
|
| 34 |
|
difeq1 |
|
| 35 |
34
|
prodeq1d |
|
| 36 |
35
|
oveq2d |
|
| 37 |
36
|
sumeq2sdv |
|
| 38 |
33 37
|
eqtrd |
|
| 39 |
38
|
mpteq2dv |
|
| 40 |
32 39
|
eqeq12d |
|
| 41 |
29 40
|
imbi12d |
|
| 42 |
|
sseq1 |
|
| 43 |
42
|
anbi2d |
|
| 44 |
|
prodeq1 |
|
| 45 |
44
|
mpteq2dv |
|
| 46 |
45
|
oveq2d |
|
| 47 |
|
sumeq1 |
|
| 48 |
|
difeq1 |
|
| 49 |
48
|
prodeq1d |
|
| 50 |
49
|
oveq2d |
|
| 51 |
50
|
sumeq2sdv |
|
| 52 |
47 51
|
eqtrd |
|
| 53 |
52
|
mpteq2dv |
|
| 54 |
46 53
|
eqeq12d |
|
| 55 |
43 54
|
imbi12d |
|
| 56 |
|
sseq1 |
|
| 57 |
56
|
anbi2d |
|
| 58 |
|
prodeq1 |
|
| 59 |
58
|
mpteq2dv |
|
| 60 |
59
|
oveq2d |
|
| 61 |
|
sumeq1 |
|
| 62 |
|
difeq1 |
|
| 63 |
62
|
prodeq1d |
|
| 64 |
63
|
oveq2d |
|
| 65 |
64
|
sumeq2sdv |
|
| 66 |
61 65
|
eqtrd |
|
| 67 |
66
|
mpteq2dv |
|
| 68 |
60 67
|
eqeq12d |
|
| 69 |
57 68
|
imbi12d |
|
| 70 |
|
prod0 |
|
| 71 |
70
|
mpteq2i |
|
| 72 |
71
|
oveq2i |
|
| 73 |
72
|
a1i |
|
| 74 |
4
|
oveq1i |
|
| 75 |
3 74
|
eqtri |
|
| 76 |
6 75
|
eleqtrdi |
|
| 77 |
|
1cnd |
|
| 78 |
5 76 77
|
dvmptconst |
|
| 79 |
|
sum0 |
|
| 80 |
79
|
eqcomi |
|
| 81 |
80
|
mpteq2i |
|
| 82 |
81
|
a1i |
|
| 83 |
73 78 82
|
3eqtrd |
|
| 84 |
83
|
adantr |
|
| 85 |
|
simp3 |
|
| 86 |
|
simp1r |
|
| 87 |
|
ssun1 |
|
| 88 |
|
sstr2 |
|
| 89 |
87 88
|
ax-mp |
|
| 90 |
89
|
anim2i |
|
| 91 |
90
|
adantl |
|
| 92 |
|
simpl |
|
| 93 |
91 92
|
mpd |
|
| 94 |
93
|
3adant1 |
|
| 95 |
|
nfv |
|
| 96 |
|
nfcv |
|
| 97 |
|
nfcv |
|
| 98 |
|
nfmpt1 |
|
| 99 |
96 97 98
|
nfov |
|
| 100 |
|
nfmpt1 |
|
| 101 |
99 100
|
nfeq |
|
| 102 |
95 101
|
nfan |
|
| 103 |
|
nfv |
|
| 104 |
1 103
|
nfan |
|
| 105 |
|
nfv |
|
| 106 |
104 105
|
nfan |
|
| 107 |
|
nfcv |
|
| 108 |
|
nfcv |
|
| 109 |
|
nfcv |
|
| 110 |
|
nfcv |
|
| 111 |
110
|
nfcprod1 |
|
| 112 |
109 111
|
nfmpt |
|
| 113 |
107 108 112
|
nfov |
|
| 114 |
|
nfcv |
|
| 115 |
|
nfcv |
|
| 116 |
|
nfcv |
|
| 117 |
116
|
nfcprod1 |
|
| 118 |
114 115 117
|
nfov |
|
| 119 |
110 118
|
nfsum |
|
| 120 |
109 119
|
nfmpt |
|
| 121 |
113 120
|
nfeq |
|
| 122 |
106 121
|
nfan |
|
| 123 |
|
nfv |
|
| 124 |
2 123
|
nfan |
|
| 125 |
|
nfv |
|
| 126 |
124 125
|
nfan |
|
| 127 |
|
nfcv |
|
| 128 |
|
nfcv |
|
| 129 |
|
nfcv |
|
| 130 |
129
|
nfsum1 |
|
| 131 |
128 130
|
nfmpt |
|
| 132 |
127 131
|
nfeq |
|
| 133 |
126 132
|
nfan |
|
| 134 |
|
nfcsb1v |
|
| 135 |
|
nfcsb1v |
|
| 136 |
|
simpl |
|
| 137 |
136
|
ad2antrr |
|
| 138 |
137 8
|
syl3an1 |
|
| 139 |
7
|
ad3antrrr |
|
| 140 |
89
|
adantl |
|
| 141 |
140
|
ad2antrr |
|
| 142 |
139 141
|
ssfid |
|
| 143 |
|
vex |
|
| 144 |
143
|
a1i |
|
| 145 |
|
simplr |
|
| 146 |
|
simpllr |
|
| 147 |
5
|
ad3antrrr |
|
| 148 |
137
|
ad2antrr |
|
| 149 |
141
|
ad2antrr |
|
| 150 |
|
simpr |
|
| 151 |
149 150
|
sseldd |
|
| 152 |
|
simplr |
|
| 153 |
|
nfv |
|
| 154 |
|
nfv |
|
| 155 |
1 153 154
|
nf3an |
|
| 156 |
|
nfv |
|
| 157 |
155 156
|
nfim |
|
| 158 |
|
eleq1w |
|
| 159 |
158
|
3anbi2d |
|
| 160 |
11
|
eleq1d |
|
| 161 |
159 160
|
imbi12d |
|
| 162 |
157 161 9
|
chvarfv |
|
| 163 |
148 151 152 162
|
syl3anc |
|
| 164 |
|
simpr |
|
| 165 |
136
|
adantr |
|
| 166 |
|
id |
|
| 167 |
|
vsnid |
|
| 168 |
|
elun2 |
|
| 169 |
167 168
|
mp1i |
|
| 170 |
166 169
|
sseldd |
|
| 171 |
170
|
ad2antlr |
|
| 172 |
|
simpr |
|
| 173 |
|
nfv |
|
| 174 |
|
nfv |
|
| 175 |
2 173 174
|
nf3an |
|
| 176 |
135
|
nfel1 |
|
| 177 |
175 176
|
nfim |
|
| 178 |
|
eleq1w |
|
| 179 |
178
|
3anbi2d |
|
| 180 |
|
csbeq1a |
|
| 181 |
180
|
eleq1d |
|
| 182 |
179 181
|
imbi12d |
|
| 183 |
177 182 162
|
chvarfv |
|
| 184 |
165 171 172 183
|
syl3anc |
|
| 185 |
184
|
ad4ant14 |
|
| 186 |
2 173
|
nfan |
|
| 187 |
|
nfcv |
|
| 188 |
128 135
|
nfmpt |
|
| 189 |
187 188
|
nfeq |
|
| 190 |
186 189
|
nfim |
|
| 191 |
178
|
anbi2d |
|
| 192 |
|
csbeq1 |
|
| 193 |
192
|
mpteq2dv |
|
| 194 |
193
|
oveq2d |
|
| 195 |
180
|
mpteq2dv |
|
| 196 |
194 195
|
eqeq12d |
|
| 197 |
191 196
|
imbi12d |
|
| 198 |
1 153
|
nfan |
|
| 199 |
|
nfcsb1v |
|
| 200 |
109 199
|
nfmpt |
|
| 201 |
107 108 200
|
nfov |
|
| 202 |
|
nfcv |
|
| 203 |
201 202
|
nfeq |
|
| 204 |
198 203
|
nfim |
|
| 205 |
158
|
anbi2d |
|
| 206 |
|
csbeq1a |
|
| 207 |
206
|
mpteq2dv |
|
| 208 |
207
|
oveq2d |
|
| 209 |
11
|
mpteq2dv |
|
| 210 |
208 209
|
eqeq12d |
|
| 211 |
205 210
|
imbi12d |
|
| 212 |
204 211 10
|
chvarfv |
|
| 213 |
190 197 212
|
chvarfv |
|
| 214 |
170 213
|
sylan2 |
|
| 215 |
214
|
ad2antrr |
|
| 216 |
|
csbeq1a |
|
| 217 |
102 122 133 134 135 138 142 144 145 146 147 163 164 185 215 216 180
|
dvmptfprodlem |
|
| 218 |
85 86 94 217
|
syl21anc |
|
| 219 |
218
|
3exp |
|
| 220 |
27 41 55 69 84 219
|
findcard2s |
|
| 221 |
7 13 220
|
sylc |
|