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	$$⊢A\in ℂ$$
Assertion	absgt0i	$$⊢A\ne 0\leftrightarrow 0<\left|A\right|$$

Proof

Step	Hyp	Ref	Expression
1		absvalsqi.1	$$⊢A\in ℂ$$
2		absgt0	$$⊢A\in ℂ\to \left(A\ne 0\leftrightarrow 0<\left|A\right|\right)$$
3	1 2	ax-mp	$$⊢A\ne 0\leftrightarrow 0<\left|A\right|$$