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Metamath Proof Explorer

Theorem sqsqrti

Description: Square of square root. (Contributed by NM, 11-Aug-1999)

		Ref	Expression
	Hypothesis	sqrtthi.1	$⊢ A \in ℝ$
	Assertion	sqsqrti	$⊢ 0 \leq A \to {\sqrt{A}}^{2} = A$

Step	Hyp	Ref	Expression
1		sqrtthi.1	$⊢ A \in ℝ$
2		resqrtth	$⊢ (A \in ℝ \land 0 \leq A) \to {\sqrt{A}}^{2} = A$
3	1 2	mpan	$⊢ 0 \leq A \to {\sqrt{A}}^{2} = A$