Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
|
ifeq1 |
|
3 |
2
|
alimi |
|
4 |
|
alral |
|
5 |
3 4
|
syl |
|
6 |
|
mpteq12 |
|
7 |
1 5 6
|
sylancr |
|
8 |
7
|
seqeq3d |
|
9 |
8
|
breq1d |
|
10 |
9
|
anbi2d |
|
11 |
10
|
exbidv |
|
12 |
11
|
rexbidv |
|
13 |
7
|
seqeq3d |
|
14 |
13
|
breq1d |
|
15 |
12 14
|
3anbi23d |
|
16 |
15
|
rexbidv |
|
17 |
|
csbeq2 |
|
18 |
17
|
mpteq2dv |
|
19 |
18
|
seqeq3d |
|
20 |
19
|
fveq1d |
|
21 |
20
|
eqeq2d |
|
22 |
21
|
anbi2d |
|
23 |
22
|
exbidv |
|
24 |
23
|
rexbidv |
|
25 |
16 24
|
orbi12d |
|
26 |
25
|
iotabidv |
|
27 |
|
df-prod |
|
28 |
|
df-prod |
|
29 |
26 27 28
|
3eqtr4g |
|