Step |
Hyp |
Ref |
Expression |
1 |
|
divdivdiv |
|- ( ( ( A e. CC /\ ( C e. CC /\ C =/= 0 ) ) /\ ( ( B e. CC /\ B =/= 0 ) /\ ( C e. CC /\ C =/= 0 ) ) ) -> ( ( A / C ) / ( B / C ) ) = ( ( A x. C ) / ( C x. B ) ) ) |
2 |
1
|
3impdir |
|- ( ( A e. CC /\ ( B e. CC /\ B =/= 0 ) /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A / C ) / ( B / C ) ) = ( ( A x. C ) / ( C x. B ) ) ) |
3 |
|
mulcom |
|- ( ( A e. CC /\ C e. CC ) -> ( A x. C ) = ( C x. A ) ) |
4 |
3
|
adantrr |
|- ( ( A e. CC /\ ( C e. CC /\ C =/= 0 ) ) -> ( A x. C ) = ( C x. A ) ) |
5 |
4
|
3adant2 |
|- ( ( A e. CC /\ ( B e. CC /\ B =/= 0 ) /\ ( C e. CC /\ C =/= 0 ) ) -> ( A x. C ) = ( C x. A ) ) |
6 |
5
|
oveq1d |
|- ( ( A e. CC /\ ( B e. CC /\ B =/= 0 ) /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A x. C ) / ( C x. B ) ) = ( ( C x. A ) / ( C x. B ) ) ) |
7 |
|
divcan5 |
|- ( ( A e. CC /\ ( B e. CC /\ B =/= 0 ) /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( C x. A ) / ( C x. B ) ) = ( A / B ) ) |
8 |
2 6 7
|
3eqtrd |
|- ( ( A e. CC /\ ( B e. CC /\ B =/= 0 ) /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A / C ) / ( B / C ) ) = ( A / B ) ) |