Theorem sqgt0d

Description: The square of a nonzero real is positive. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	sqgt0d.1	$$⊢\phi \to A\in ℝ$$
	sqgt0d.2	$$⊢\phi \to A\ne 0$$
Assertion	sqgt0d	$$⊢\phi \to 0<A^2$$

Proof

Step	Hyp	Ref	Expression
1		sqgt0d.1	$$⊢\phi \to A\in ℝ$$
2		sqgt0d.2	$$⊢\phi \to A\ne 0$$
3		sqgt0	$$⊢\left(A\in ℝ\wedge A\ne 0\right)\to 0<A^2$$
4	1 2 3	syl2anc	$$⊢\phi \to 0<A^2$$