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 |
|