Description: Cross-multiply in an equality of ratios. (Contributed by Mario Carneiro, 23-Feb-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | divmuleq | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divcl | |
|
2 | 1 | 3expb | |
3 | 2 | ad2ant2r | |
4 | divcl | |
|
5 | 4 | 3expb | |
6 | 5 | ad2ant2l | |
7 | mulcl | |
|
8 | 7 | ad2ant2r | |
9 | mulne0 | |
|
10 | 8 9 | jca | |
11 | 10 | adantl | |
12 | mulcan2 | |
|
13 | 3 6 11 12 | syl3anc | |
14 | simprll | |
|
15 | simprrl | |
|
16 | 3 14 15 | mulassd | |
17 | divcan1 | |
|
18 | 17 | 3expb | |
19 | 18 | ad2ant2r | |
20 | 19 | oveq1d | |
21 | 16 20 | eqtr3d | |
22 | 14 15 | mulcomd | |
23 | 22 | oveq2d | |
24 | 6 15 14 | mulassd | |
25 | divcan1 | |
|
26 | 25 | 3expb | |
27 | 26 | ad2ant2l | |
28 | 27 | oveq1d | |
29 | 23 24 28 | 3eqtr2d | |
30 | 21 29 | eqeq12d | |
31 | 13 30 | bitr3d | |