Step |
Hyp |
Ref |
Expression |
1 |
|
simprl |
|
2 |
|
simpl3 |
|
3 |
1 2
|
mulscld |
|
4 |
|
oveq1 |
|
5 |
4
|
adantl |
|
6 |
5
|
adantl |
|
7 |
|
simpl1 |
|
8 |
7 1 2
|
mulsassd |
|
9 |
2
|
mulslidd |
|
10 |
6 8 9
|
3eqtr3d |
|
11 |
|
oveq2 |
|
12 |
11
|
eqeq1d |
|
13 |
12
|
rspcev |
|
14 |
3 10 13
|
syl2anc |
|
15 |
14
|
rexlimdvaa |
|
16 |
15
|
imp |
|
17 |
|
oveq2 |
|
18 |
17
|
eqeq1d |
|
19 |
18
|
cbvrexvw |
|
20 |
19
|
anbi2i |
|
21 |
|
oveq2 |
|
22 |
21
|
eqeq1d |
|
23 |
22
|
cbvrexvw |
|
24 |
16 20 23
|
3imtr4i |
|