Theorem sqsqrti

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

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

Proof

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