Description: A cancellation law for division. (Eliminates a hypothesis of divcan3i with the weak deduction theorem.) (Contributed by NM, 3-Feb-2004)
Ref | Expression | ||
---|---|---|---|
Hypotheses | divclz.1 | |- A e. CC |
|
divclz.2 | |- B e. CC |
||
Assertion | divcan3zi | |- ( B =/= 0 -> ( ( B x. A ) / B ) = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | |- A e. CC |
|
2 | divclz.2 | |- B e. CC |
|
3 | divcan3 | |- ( ( A e. CC /\ B e. CC /\ B =/= 0 ) -> ( ( B x. A ) / B ) = A ) |
|
4 | 1 2 3 | mp3an12 | |- ( B =/= 0 -> ( ( B x. A ) / B ) = A ) |