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
|
a1d |
|
66 |
65
|
ralrimiv |
|
67 |
66
|
sumeq2d |
|
68 |
61 67
|
eqtrd |
|
69 |
68
|
mpteq2dv |
|
70 |
60 69
|
eqeq12d |
|
71 |
57 70
|
imbi12d |
|
72 |
|
prod0 |
|
73 |
72
|
mpteq2i |
|
74 |
73
|
oveq2i |
|
75 |
74
|
a1i |
|
76 |
4
|
oveq1i |
|
77 |
3 76
|
eqtri |
|
78 |
6 77
|
eleqtrdi |
|
79 |
|
1cnd |
|
80 |
5 78 79
|
dvmptconst |
|
81 |
|
sum0 |
|
82 |
81
|
eqcomi |
|
83 |
82
|
mpteq2i |
|
84 |
83
|
a1i |
|
85 |
75 80 84
|
3eqtrd |
|
86 |
85
|
adantr |
|
87 |
|
simp3 |
|
88 |
|
simp1r |
|
89 |
|
simpl |
|
90 |
|
ssun1 |
|
91 |
|
sstr2 |
|
92 |
90 91
|
ax-mp |
|
93 |
92
|
adantl |
|
94 |
89 93
|
jca |
|
95 |
94
|
adantl |
|
96 |
|
simpl |
|
97 |
95 96
|
mpd |
|
98 |
97
|
3adant1 |
|
99 |
|
nfv |
|
100 |
|
nfcv |
|
101 |
|
nfcv |
|
102 |
|
nfmpt1 |
|
103 |
100 101 102
|
nfov |
|
104 |
|
nfmpt1 |
|
105 |
103 104
|
nfeq |
|
106 |
99 105
|
nfan |
|
107 |
|
nfv |
|
108 |
1 107
|
nfan |
|
109 |
|
nfv |
|
110 |
108 109
|
nfan |
|
111 |
|
nfcv |
|
112 |
|
nfcv |
|
113 |
|
nfcv |
|
114 |
|
nfcv |
|
115 |
114
|
nfcprod1 |
|
116 |
113 115
|
nfmpt |
|
117 |
111 112 116
|
nfov |
|
118 |
|
nfcv |
|
119 |
|
nfcv |
|
120 |
|
nfcv |
|
121 |
120
|
nfcprod1 |
|
122 |
118 119 121
|
nfov |
|
123 |
114 122
|
nfsum |
|
124 |
113 123
|
nfmpt |
|
125 |
117 124
|
nfeq |
|
126 |
110 125
|
nfan |
|
127 |
|
nfv |
|
128 |
2 127
|
nfan |
|
129 |
|
nfv |
|
130 |
128 129
|
nfan |
|
131 |
|
nfcv |
|
132 |
|
nfcv |
|
133 |
|
nfcv |
|
134 |
133
|
nfsum1 |
|
135 |
132 134
|
nfmpt |
|
136 |
131 135
|
nfeq |
|
137 |
130 136
|
nfan |
|
138 |
|
nfcsb1v |
|
139 |
|
nfcsb1v |
|
140 |
89
|
ad2antrr |
|
141 |
140
|
3ad2ant1 |
|
142 |
|
simp2 |
|
143 |
|
simp3 |
|
144 |
141 142 143 8
|
syl3anc |
|
145 |
140 7
|
syl |
|
146 |
93
|
ad2antrr |
|
147 |
|
ssfi |
|
148 |
145 146 147
|
syl2anc |
|
149 |
|
vex |
|
150 |
149
|
a1i |
|
151 |
|
simplr |
|
152 |
|
simpllr |
|
153 |
5
|
ad3antrrr |
|
154 |
140
|
ad2antrr |
|
155 |
146
|
ad2antrr |
|
156 |
|
simpr |
|
157 |
155 156
|
sseldd |
|
158 |
|
simplr |
|
159 |
|
nfv |
|
160 |
|
nfv |
|
161 |
1 159 160
|
nf3an |
|
162 |
|
nfv |
|
163 |
161 162
|
nfim |
|
164 |
|
eleq1w |
|
165 |
164
|
3anbi2d |
|
166 |
11
|
eleq1d |
|
167 |
165 166
|
imbi12d |
|
168 |
163 167 9
|
chvarfv |
|
169 |
154 157 158 168
|
syl3anc |
|
170 |
|
simpr |
|
171 |
89
|
adantr |
|
172 |
|
id |
|
173 |
149
|
snid |
|
174 |
|
elun2 |
|
175 |
173 174
|
ax-mp |
|
176 |
175
|
a1i |
|
177 |
172 176
|
sseldd |
|
178 |
177
|
ad2antlr |
|
179 |
|
simpr |
|
180 |
|
nfv |
|
181 |
|
nfv |
|
182 |
2 180 181
|
nf3an |
|
183 |
|
nfcv |
|
184 |
139 183
|
nfel |
|
185 |
182 184
|
nfim |
|
186 |
|
eleq1w |
|
187 |
186
|
3anbi2d |
|
188 |
|
csbeq1a |
|
189 |
188
|
eleq1d |
|
190 |
187 189
|
imbi12d |
|
191 |
185 190 168
|
chvarfv |
|
192 |
171 178 179 191
|
syl3anc |
|
193 |
192
|
adantlr |
|
194 |
193
|
adantlr |
|
195 |
2 180
|
nfan |
|
196 |
|
nfcv |
|
197 |
132 139
|
nfmpt |
|
198 |
196 197
|
nfeq |
|
199 |
195 198
|
nfim |
|
200 |
186
|
anbi2d |
|
201 |
|
csbeq1a |
|
202 |
|
csbcow |
|
203 |
202
|
a1i |
|
204 |
201 203
|
eqtrd |
|
205 |
204
|
mpteq2dv |
|
206 |
205
|
oveq2d |
|
207 |
188
|
mpteq2dv |
|
208 |
206 207
|
eqeq12d |
|
209 |
200 208
|
imbi12d |
|
210 |
1 159
|
nfan |
|
211 |
|
nfcsb1v |
|
212 |
113 211
|
nfmpt |
|
213 |
111 112 212
|
nfov |
|
214 |
|
nfcv |
|
215 |
213 214
|
nfeq |
|
216 |
210 215
|
nfim |
|
217 |
164
|
anbi2d |
|
218 |
|
csbeq1a |
|
219 |
218
|
mpteq2dv |
|
220 |
219
|
oveq2d |
|
221 |
11
|
idi |
|
222 |
221
|
mpteq2dv |
|
223 |
220 222
|
eqeq12d |
|
224 |
217 223
|
imbi12d |
|
225 |
216 224 10
|
chvarfv |
|
226 |
199 209 225
|
chvarfv |
|
227 |
177 226
|
sylan2 |
|
228 |
227
|
ad2antrr |
|
229 |
|
csbeq1a |
|
230 |
106 126 137 138 139 144 148 150 151 152 153 169 170 194 228 229 188
|
dvmptfprodlem |
|
231 |
87 88 98 230
|
syl21anc |
|
232 |
231
|
3exp |
|
233 |
27 41 55 71 86 232
|
findcard2s |
|
234 |
7 13 233
|
sylc |
|