Theorem sqsqrti

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

	Ref	Expression
Hypothesis	sqrtthi.1	⊢ 𝐴 ∈ ℝ
Assertion	sqsqrti	⊢ ( 0 ≤ 𝐴 → ( ( √ ‘ 𝐴 ) ↑ 2 ) = 𝐴 )

Proof

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