Description: Division into a reciprocal. (Contributed by NM, 19-Oct-2007)
Ref | Expression | ||
---|---|---|---|
Assertion | recdiv2 | |- ( ( ( A e. CC /\ A =/= 0 ) /\ ( B e. CC /\ B =/= 0 ) ) -> ( ( 1 / A ) / B ) = ( 1 / ( A x. B ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn | |- 1 e. CC |
|
2 | divdiv1 | |- ( ( 1 e. CC /\ ( A e. CC /\ A =/= 0 ) /\ ( B e. CC /\ B =/= 0 ) ) -> ( ( 1 / A ) / B ) = ( 1 / ( A x. B ) ) ) |
|
3 | 1 2 | mp3an1 | |- ( ( ( A e. CC /\ A =/= 0 ) /\ ( B e. CC /\ B =/= 0 ) ) -> ( ( 1 / A ) / B ) = ( 1 / ( A x. B ) ) ) |