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Metamath Proof Explorer

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	$⊢ A \neq 0 \to 0 < A^{2}$

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