Theorem sqrtmsqi

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

	Ref	Expression
Hypothesis	sqrtthi.1	⊢ 𝐴 ∈ ℝ
Assertion	sqrtmsqi	⊢ ( 0 ≤ 𝐴 → ( √ ‘ ( 𝐴 · 𝐴 ) ) = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	⊢ 𝐴 ∈ ℝ
2		sqrtmsq	⊢ ( ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ) → ( √ ‘ ( 𝐴 · 𝐴 ) ) = 𝐴 )
3	1 2	mpan	⊢ ( 0 ≤ 𝐴 → ( √ ‘ ( 𝐴 · 𝐴 ) ) = 𝐴 )