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	$$⊢0\le A\to \sqrt{A}\sqrt{A}=A$$

Proof

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