Description: The absolute value of a nonzero number is positive. Remark in Apostol p. 363. (Contributed by NM, 1-Oct-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | absvalsqi.1 | |- A e. CC |
|
Assertion | absgt0i | |- ( A =/= 0 <-> 0 < ( abs ` A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | absvalsqi.1 | |- A e. CC |
|
2 | absgt0 | |- ( A e. CC -> ( A =/= 0 <-> 0 < ( abs ` A ) ) ) |
|
3 | 1 2 | ax-mp | |- ( A =/= 0 <-> 0 < ( abs ` A ) ) |