Theorem sqgt0i

Description: The square of a nonzero real is positive. (Contributed by NM, 17-Sep-1999)

	Ref	Expression
Hypothesis	resqcl.1	$$⊢A\in ℝ$$
Assertion	sqgt0i	$$⊢A\ne 0\to 0<A^2$$

Proof

Step	Hyp	Ref	Expression
1		resqcl.1	$$⊢A\in ℝ$$
2		sqgt0	$$⊢\left(A\in ℝ\wedge A\ne 0\right)\to 0<A^2$$
3	1 2	mpan	$$⊢A\ne 0\to 0<A^2$$