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Metamath Proof Explorer

Theorem sqrtge0i

Description: The square root of a nonnegative real is nonnegative. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)

Ref Expression
Hypothesis sqrtthi.1 ⊢ 𝐴 ∈ ℝ
Assertion sqrtge0i ( 0 ≤ 𝐴 → 0 ≤ ( √ ‘ 𝐴 ) )

Proof

Step Hyp Ref Expression
1 sqrtthi.1 ⊢ 𝐴 ∈ ℝ
2 sqrtge0 ⊢ ( ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ) → 0 ≤ ( √ ‘ 𝐴 ) )
3 1 2 mpan ⊢ ( 0 ≤ 𝐴 → 0 ≤ ( √ ‘ 𝐴 ) )