Description: Closure law for reciprocal. (Contributed by NM, 30-Apr-2005)
Ref | Expression | ||
---|---|---|---|
Hypothesis | divclz.1 | |- A e. CC |
|
Assertion | recclzi | |- ( A =/= 0 -> ( 1 / A ) e. CC ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | divclz.1 | |- A e. CC |
|
2 | reccl | |- ( ( A e. CC /\ A =/= 0 ) -> ( 1 / A ) e. CC ) |
|
3 | 1 2 | mpan | |- ( A =/= 0 -> ( 1 / A ) e. CC ) |