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Metamath Proof Explorer

Theorem sqrtgt0d

Description: The square root of a positive real is positive. (Contributed by Mario Carneiro, 29-May-2016)

		Ref	Expression
	Hypothesis	sqrgt0d.1	$⊢ φ \to A \in ℝ^{+}$
	Assertion	sqrtgt0d	$⊢ φ \to 0 < \sqrt{A}$

Step	Hyp	Ref	Expression
1		sqrgt0d.1	$⊢ φ \to A \in ℝ^{+}$
2	1	rpsqrtcld	$⊢ φ \to \sqrt{A} \in ℝ^{+}$
3	2	rpgt0d	$⊢ φ \to 0 < \sqrt{A}$