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Metamath Proof Explorer

Theorem sqrtthi

Description: Square root theorem. Theorem I.35 of Apostol p. 29. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)

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

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