Description: Multiplication of a number and its reciprocal. (Contributed by NM, 9-Feb-1995)
Ref | Expression | ||
---|---|---|---|
Hypotheses | divclz.1 | |- A e. CC |
|
reccl.2 | |- A =/= 0 |
||
Assertion | recidi | |- ( A x. ( 1 / A ) ) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | |- A e. CC |
|
2 | reccl.2 | |- A =/= 0 |
|
3 | 1 | recidzi | |- ( A =/= 0 -> ( A x. ( 1 / A ) ) = 1 ) |
4 | 2 3 | ax-mp | |- ( A x. ( 1 / A ) ) = 1 |