Theorem absgt0i

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 ) )

Proof

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 ) )