Description: Relationship between division and multiplication. (Contributed by NM, 7-Feb-2006)
Ref | Expression | ||
---|---|---|---|
Assertion | divmul2 | |- ( ( A e. CC /\ B e. CC /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A / C ) = B <-> A = ( C x. B ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divmul | |- ( ( A e. CC /\ B e. CC /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A / C ) = B <-> ( C x. B ) = A ) ) |
|
2 | eqcom | |- ( ( C x. B ) = A <-> A = ( C x. B ) ) |
|
3 | 1 2 | bitrdi | |- ( ( A e. CC /\ B e. CC /\ ( C e. CC /\ C =/= 0 ) ) -> ( ( A / C ) = B <-> A = ( C x. B ) ) ) |