Theorem sqrtmsqi

Description: Square root of square. (Contributed by NM, 2-Aug-1999)

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

Proof

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