Description: A number is equal to the reciprocal of its reciprocal. Theorem I.10 of Apostol p. 18. (Contributed by NM, 9-Feb-1995)
Ref | Expression | ||
---|---|---|---|
Hypotheses | divclz.1 | |- A e. CC |
|
reccl.2 | |- A =/= 0 |
||
Assertion | recreci | |- ( 1 / ( 1 / A ) ) = A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | |- A e. CC |
|
2 | reccl.2 | |- A =/= 0 |
|
3 | recrec | |- ( ( A e. CC /\ A =/= 0 ) -> ( 1 / ( 1 / A ) ) = A ) |
|
4 | 1 2 3 | mp2an | |- ( 1 / ( 1 / A ) ) = A |