This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem sqgt0d

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

Step	Hyp	Ref	Expression
1		sqgt0d.1	$⊢ φ \to A \in ℝ$
2		sqgt0d.2	$⊢ φ \to A \neq 0$
3		sqgt0	$⊢ (A \in ℝ \land A \neq 0) \to 0 < A^{2}$
4	1 2 3	syl2anc	$⊢ φ \to 0 < A^{2}$